Leibniz Algebras Associated with Representations of Euclidean Lie Algebra View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-01-04

AUTHORS

J. Q. Adashev, B. A. Omirov, S. Uguz

ABSTRACT

In the present paper we describe Leibniz algebras with three-dimensional Euclidean Lie algebra e(2) as its liezation. Moreover, it is assumed that the ideal generated by the squares of elements of an algebra (denoted by I) as a right e(2)-module is associated to representations of e(2) in sl2(ℂ)⊕sl2(ℂ),sl3(ℂ) and sp4(ℂ). Furthermore, we present the classification of Leibniz algebras with general Euclidean Lie algebra e(n) as its liezation I being an (n + 1)-dimensional right e(n)-module defined by transformations of matrix realization of e(n). Finally, we extend the notion of a Fock module over Heisenberg Lie algebra to the case of Diamond Lie algebra Dk and describe the structure of Leibniz algebras with corresponding Lie algebra Dk and with the ideal I considered as a Fock Dk-module. More... »

PAGES

1-17

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10468-018-09849-1

DOI

http://dx.doi.org/10.1007/s10468-018-09849-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111156529


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Academy of Sciences Republic of Uzbekistan", 
          "id": "https://www.grid.ac/institutes/grid.419209.7", 
          "name": [
            "Institute of Mathematics, Uzbekistan Academy of Sciences, M.Ulugbek str. 81, 100170, Tashkent, Uzbekistan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Adashev", 
        "givenName": "J. Q.", 
        "id": "sg:person.016537505601.61", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016537505601.61"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "National University of Uzbekistan", 
          "id": "https://www.grid.ac/institutes/grid.23471.33", 
          "name": [
            "National University of Uzbekistan, University str. 4, 100174, Tashkent, Uzbekistan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Omirov", 
        "givenName": "B. A.", 
        "id": "sg:person.014500267073.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014500267073.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Harran University", 
          "id": "https://www.grid.ac/institutes/grid.411999.d", 
          "name": [
            "Department of Mathematics, Arts and Sciences Faculty Harran University, 63120, \u015eanliurfa, Turkey"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Uguz", 
        "givenName": "S.", 
        "id": "sg:person.014255257731.86", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014255257731.86"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.geomphys.2015.08.002", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002975972"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00927879608825618", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003024636"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/crll.1995.467.67", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008404131"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/1751-8113/43/8/085204", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013875466"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jalgebra.2015.12.018", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027012688"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03081087.2012.703194", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029802606"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00927870601168814", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031440246"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jalgebra.2006.01.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033156624"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.4880195", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035001183"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.laa.2012.11.023", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036484326"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00927872.2010.551532", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040093986"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0004972711002954", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050336165"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.3316063", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057935678"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.3316063", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057935678"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1088/0305-4470/14/6/019", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059065699"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.5209/rev_rema.2006.v19.n1.16652", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072708625"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-01-04", 
    "datePublishedReg": "2019-01-04", 
    "description": "In the present paper we describe Leibniz algebras with three-dimensional Euclidean Lie algebra e(2) as its liezation. Moreover, it is assumed that the ideal generated by the squares of elements of an algebra (denoted by I) as a right e(2)-module is associated to representations of e(2) in sl2(\u2102)\u2295sl2(\u2102),sl3(\u2102) and sp4(\u2102). Furthermore, we present the classification of Leibniz algebras with general Euclidean Lie algebra e(n) as its liezation I being an (n + 1)-dimensional right e(n)-module defined by transformations of matrix realization of e(n). Finally, we extend the notion of a Fock module over Heisenberg Lie algebra to the case of Diamond Lie algebra Dk and describe the structure of Leibniz algebras with corresponding Lie algebra Dk and with the ideal I considered as a Fock Dk-module.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10468-018-09849-1", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1136385", 
        "issn": [
          "1386-923X", 
          "1572-9079"
        ], 
        "name": "Algebras and Representation Theory", 
        "type": "Periodical"
      }
    ], 
    "name": "Leibniz Algebras Associated with Representations of Euclidean Lie Algebra", 
    "pagination": "1-17", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "e2e774678314fe76d913896839931807105f5f2718712c7bd2fac458abb13a24"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10468-018-09849-1"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1111156529"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10468-018-09849-1", 
      "https://app.dimensions.ai/details/publication/pub.1111156529"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T08:34", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000311_0000000311/records_55451_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs10468-018-09849-1"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10468-018-09849-1'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10468-018-09849-1'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10468-018-09849-1'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10468-018-09849-1'


 

This table displays all metadata directly associated to this object as RDF triples.

120 TRIPLES      21 PREDICATES      39 URIs      16 LITERALS      5 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10468-018-09849-1 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N744ccf888a164be6855562fbdcc579c2
4 schema:citation https://doi.org/10.1016/j.geomphys.2015.08.002
5 https://doi.org/10.1016/j.jalgebra.2006.01.004
6 https://doi.org/10.1016/j.jalgebra.2015.12.018
7 https://doi.org/10.1016/j.laa.2012.11.023
8 https://doi.org/10.1017/s0004972711002954
9 https://doi.org/10.1063/1.3316063
10 https://doi.org/10.1063/1.4880195
11 https://doi.org/10.1080/00927870601168814
12 https://doi.org/10.1080/00927872.2010.551532
13 https://doi.org/10.1080/00927879608825618
14 https://doi.org/10.1080/03081087.2012.703194
15 https://doi.org/10.1088/0305-4470/14/6/019
16 https://doi.org/10.1088/1751-8113/43/8/085204
17 https://doi.org/10.1515/crll.1995.467.67
18 https://doi.org/10.5209/rev_rema.2006.v19.n1.16652
19 schema:datePublished 2019-01-04
20 schema:datePublishedReg 2019-01-04
21 schema:description In the present paper we describe Leibniz algebras with three-dimensional Euclidean Lie algebra e(2) as its liezation. Moreover, it is assumed that the ideal generated by the squares of elements of an algebra (denoted by I) as a right e(2)-module is associated to representations of e(2) in sl2(ℂ)⊕sl2(ℂ),sl3(ℂ) and sp4(ℂ). Furthermore, we present the classification of Leibniz algebras with general Euclidean Lie algebra e(n) as its liezation I being an (n + 1)-dimensional right e(n)-module defined by transformations of matrix realization of e(n). Finally, we extend the notion of a Fock module over Heisenberg Lie algebra to the case of Diamond Lie algebra Dk and describe the structure of Leibniz algebras with corresponding Lie algebra Dk and with the ideal I considered as a Fock Dk-module.
22 schema:genre research_article
23 schema:inLanguage en
24 schema:isAccessibleForFree true
25 schema:isPartOf sg:journal.1136385
26 schema:name Leibniz Algebras Associated with Representations of Euclidean Lie Algebra
27 schema:pagination 1-17
28 schema:productId N06c8b04571514561b6016ee6692d4113
29 N6223f6aa886c46d4b7370584942e4cad
30 Nc431daf5f9714c1c9874cab161bcd345
31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111156529
32 https://doi.org/10.1007/s10468-018-09849-1
33 schema:sdDatePublished 2019-04-11T08:34
34 schema:sdLicense https://scigraph.springernature.com/explorer/license/
35 schema:sdPublisher N7f092429ec7740d696d9624825190df2
36 schema:url https://link.springer.com/10.1007%2Fs10468-018-09849-1
37 sgo:license sg:explorer/license/
38 sgo:sdDataset articles
39 rdf:type schema:ScholarlyArticle
40 N06c8b04571514561b6016ee6692d4113 schema:name doi
41 schema:value 10.1007/s10468-018-09849-1
42 rdf:type schema:PropertyValue
43 N6223f6aa886c46d4b7370584942e4cad schema:name dimensions_id
44 schema:value pub.1111156529
45 rdf:type schema:PropertyValue
46 N744ccf888a164be6855562fbdcc579c2 rdf:first sg:person.016537505601.61
47 rdf:rest Nc7f8c054e66a45f0909f5a77ec190d7e
48 N7f092429ec7740d696d9624825190df2 schema:name Springer Nature - SN SciGraph project
49 rdf:type schema:Organization
50 Nc1cf02cc601343ea937060eaf5456eb4 rdf:first sg:person.014255257731.86
51 rdf:rest rdf:nil
52 Nc431daf5f9714c1c9874cab161bcd345 schema:name readcube_id
53 schema:value e2e774678314fe76d913896839931807105f5f2718712c7bd2fac458abb13a24
54 rdf:type schema:PropertyValue
55 Nc7f8c054e66a45f0909f5a77ec190d7e rdf:first sg:person.014500267073.48
56 rdf:rest Nc1cf02cc601343ea937060eaf5456eb4
57 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
58 schema:name Mathematical Sciences
59 rdf:type schema:DefinedTerm
60 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
61 schema:name Pure Mathematics
62 rdf:type schema:DefinedTerm
63 sg:journal.1136385 schema:issn 1386-923X
64 1572-9079
65 schema:name Algebras and Representation Theory
66 rdf:type schema:Periodical
67 sg:person.014255257731.86 schema:affiliation https://www.grid.ac/institutes/grid.411999.d
68 schema:familyName Uguz
69 schema:givenName S.
70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014255257731.86
71 rdf:type schema:Person
72 sg:person.014500267073.48 schema:affiliation https://www.grid.ac/institutes/grid.23471.33
73 schema:familyName Omirov
74 schema:givenName B. A.
75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014500267073.48
76 rdf:type schema:Person
77 sg:person.016537505601.61 schema:affiliation https://www.grid.ac/institutes/grid.419209.7
78 schema:familyName Adashev
79 schema:givenName J. Q.
80 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016537505601.61
81 rdf:type schema:Person
82 https://doi.org/10.1016/j.geomphys.2015.08.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002975972
83 rdf:type schema:CreativeWork
84 https://doi.org/10.1016/j.jalgebra.2006.01.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033156624
85 rdf:type schema:CreativeWork
86 https://doi.org/10.1016/j.jalgebra.2015.12.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027012688
87 rdf:type schema:CreativeWork
88 https://doi.org/10.1016/j.laa.2012.11.023 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036484326
89 rdf:type schema:CreativeWork
90 https://doi.org/10.1017/s0004972711002954 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050336165
91 rdf:type schema:CreativeWork
92 https://doi.org/10.1063/1.3316063 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057935678
93 rdf:type schema:CreativeWork
94 https://doi.org/10.1063/1.4880195 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035001183
95 rdf:type schema:CreativeWork
96 https://doi.org/10.1080/00927870601168814 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031440246
97 rdf:type schema:CreativeWork
98 https://doi.org/10.1080/00927872.2010.551532 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040093986
99 rdf:type schema:CreativeWork
100 https://doi.org/10.1080/00927879608825618 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003024636
101 rdf:type schema:CreativeWork
102 https://doi.org/10.1080/03081087.2012.703194 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029802606
103 rdf:type schema:CreativeWork
104 https://doi.org/10.1088/0305-4470/14/6/019 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059065699
105 rdf:type schema:CreativeWork
106 https://doi.org/10.1088/1751-8113/43/8/085204 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013875466
107 rdf:type schema:CreativeWork
108 https://doi.org/10.1515/crll.1995.467.67 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008404131
109 rdf:type schema:CreativeWork
110 https://doi.org/10.5209/rev_rema.2006.v19.n1.16652 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072708625
111 rdf:type schema:CreativeWork
112 https://www.grid.ac/institutes/grid.23471.33 schema:alternateName National University of Uzbekistan
113 schema:name National University of Uzbekistan, University str. 4, 100174, Tashkent, Uzbekistan
114 rdf:type schema:Organization
115 https://www.grid.ac/institutes/grid.411999.d schema:alternateName Harran University
116 schema:name Department of Mathematics, Arts and Sciences Faculty Harran University, 63120, Şanliurfa, Turkey
117 rdf:type schema:Organization
118 https://www.grid.ac/institutes/grid.419209.7 schema:alternateName Academy of Sciences Republic of Uzbekistan
119 schema:name Institute of Mathematics, Uzbekistan Academy of Sciences, M.Ulugbek str. 81, 100170, Tashkent, Uzbekistan
120 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...