New group-theoretic methods in quantum physics View Homepage


Ontology type: schema:MonetaryGrant     


Grant Info

YEARS

1996-1996

FUNDING AMOUNT

N/A

ABSTRACT

link has been studied between all the different types of canonical bases Gelfand-Zeitlin for finite-dimensional irreducible representations of the quantum algebra Uq (su (3)). It was clearly shown that the coefficients of such a connection, called the Weyl coefficients are equal (up to a few simple factors) q-coefficients Cancer (or q-6j symbols) quantum algebra Uq (su (2)). He developed the theory of Clebsch-Gordan coefficients (Wigner) for the quantum algebra Uq (u (3)). The canonical solution to the problem of multiplicity in the tensor product of irreducible finite-dimensional representations of the algebra u (3), proposed Biedenharnom, Lauck and Hecht and implemented in computer codes Draerom and Akiyama, was generalized to the case of quantum algebra Uq (u (3)). The method of projection operators had obtained an analytical formula for the special ( "seed") Uq (u (3)) - Wigner coefficients. This result can be used which can be used in the circuit-Draera Akiyama for other Wigner coefficients normalized for the conventional algebra U (3) and for q-deformed algebra Uq (su (3)). They were calculated and tabulated all isoscalar factors such as <(22) '(22) || (lm)> q with unit multiplicity. Found a new two-parameter deformation of the universal enveloping algebra U (g [u]) for the Lie polynomial current algebra g [u] over any simple finite-dimensional complex Lie algebra g. It is shown that such a quantum Hopf algebra can be seen as quantization of U (g [u]) in the direction of classical r-matrix, which is the sum of the simplest rational and trigonometric solutions of the Yang-Baxter classical equation, depending on the parameters. Studied classical limit elliptic algebra Aq, p (sl2) and its variant limiting Ax, h (sl2). The corresponding Lie algebra is the central extension of the algebra sl2-valued generalized (doubly) - periodic functions. Classic elliptic and trigonometric solutions of the classical Yang-Baxter equation are interpreted in terms of Lie formalism Semenov-Tyan-Shan. Presenting geometric realization of the category of finite-dimensional representations of simple Lie algebra with a tensor structure defined monodromies solutions KZ equation (kvazitenzornoy Drinfeld category). It is proved that this kvazitenzornaya category equivalent to the category of factoring modules over the ring More... »

URL

http://www.rfbr.ru/rffi/ru/project_search/o_78483

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/2008/2201", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "type": "DefinedTerm"
      }
    ], 
    "description": "link has been studied between all the different types of canonical bases Gelfand-Zeitlin for finite-dimensional irreducible representations of the quantum algebra Uq (su (3)). It was clearly shown that the coefficients of such a connection, called the Weyl coefficients are equal (up to a few simple factors) q-coefficients Cancer (or q-6j symbols) quantum algebra Uq (su (2)). He developed the theory of Clebsch-Gordan coefficients (Wigner) for the quantum algebra Uq (u (3)). The canonical solution to the problem of multiplicity in the tensor product of irreducible finite-dimensional representations of the algebra u (3), proposed Biedenharnom, Lauck and Hecht and implemented in computer codes Draerom and Akiyama, was generalized to the case of quantum algebra Uq (u (3)). The method of projection operators had obtained an analytical formula for the special ( \"seed\") Uq (u (3)) - Wigner coefficients. This result can be used which can be used in the circuit-Draera Akiyama for other Wigner coefficients normalized for the conventional algebra U (3) and for q-deformed algebra Uq (su (3)). They were calculated and tabulated all isoscalar factors such as <(22) '(22) || (lm)> q with unit multiplicity. Found a new two-parameter deformation of the universal enveloping algebra U (g [u]) for the Lie polynomial current algebra g [u] over any simple finite-dimensional complex Lie algebra g. It is shown that such a quantum Hopf algebra can be seen as\nquantization of U (g [u]) in the direction of classical r-matrix, which is the sum of the simplest rational and trigonometric solutions of the Yang-Baxter classical equation, depending on the parameters. Studied classical limit elliptic algebra Aq, p (sl2) and its variant limiting Ax, h (sl2). The corresponding Lie algebra is the central extension of the algebra sl2-valued generalized (doubly) - periodic functions. Classic elliptic and trigonometric solutions of the classical Yang-Baxter equation are interpreted in terms of Lie formalism Semenov-Tyan-Shan.\u00a0Presenting geometric realization of the category of finite-dimensional representations of simple Lie algebra with a tensor structure defined monodromies solutions KZ equation (kvazitenzornoy Drinfeld category). It is proved that this kvazitenzornaya category equivalent to the category of factoring modules over the ring", 
    "endDate": "1996-12-31T00:00:00Z", 
    "funder": {
      "id": "https://www.grid.ac/institutes/grid.452899.b", 
      "type": "Organization"
    }, 
    "id": "sg:grant.5464257", 
    "identifier": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "5464257"
        ]
      }, 
      {
        "name": "rfbr_id", 
        "type": "PropertyValue", 
        "value": [
          "96-01-01421"
        ]
      }
    ], 
    "inLanguage": [
      "ru"
    ], 
    "keywords": [
      "Shan", 
      "UQ", 
      "link", 
      "conventional algebra U", 
      "variants", 
      "analytical formula", 
      "Classic elliptic", 
      "coefficients Cancer", 
      "two-parameter deformation", 
      "elliptic algebra Aq", 
      "Hecht", 
      "METHODS", 
      "kvazitenzornoy Drinfeld category", 
      "algebra", 
      "unit multiplicity", 
      "results", 
      "coefficient", 
      "canonical solution", 
      "q-6j symbols", 
      "Biedenharnom", 
      "classical limit", 
      "parameters", 
      "cases", 
      "direction", 
      "finite-dimensional irreducible representations", 
      "tensor product", 
      "Weyl coefficients", 
      "central extension", 
      "New group-theoretic methods", 
      "Lie polynomial current algebra g", 
      "isoscalar factors", 
      "Wigner coefficients", 
      "circuit-Draera Akiyama", 
      "quantization", 
      "computer codes Draerom", 
      "multiplicity", 
      "Wigner", 
      "simple Lie algebras", 
      "kvazitenzornaya category", 
      "projection operators", 
      "theory", 
      "ring", 
      "matrix", 
      "other Wigner coefficients", 
      "simple finite-dimensional complex Lie algebra g.", 
      "finite-dimensional representations", 
      "Lie algebra", 
      "quantum physics", 
      "quantum algebra Uq", 
      "periodic functions", 
      "Akiyama", 
      "irreducible finite-dimensional representations", 
      "classical Yang-Baxter equation", 
      "Lie formalism Semenov-Tyan", 
      "seeds", 
      "terms", 
      "problem", 
      "tensor structure", 
      "quantum Hopf algebra", 
      "axes", 
      "Clebsch-Gordan coefficients", 
      "algebra U", 
      "factoring modules", 
      "monodromies solutions KZ equation", 
      "SL2", 
      "different types", 
      "sum", 
      "categories", 
      "Yang-Baxter classical equation", 
      "trigonometric solutions", 
      "Lauck", 
      "geometric realization", 
      "deformed algebra Uq", 
      "canonical bases Gelfand-Zeitlin", 
      "connection", 
      "few simple factors"
    ], 
    "name": "New group-theoretic methods in quantum physics", 
    "sameAs": [
      "https://app.dimensions.ai/details/grant/grant.5464257"
    ], 
    "sdDataset": "grants", 
    "sdDatePublished": "2019-03-07T12:53", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com.uberresearch.data.processor/core_data/20181219_192338/projects/base/rfbr_projects_7.xml.gz", 
    "startDate": "1996-01-01T00:00:00Z", 
    "type": "MonetaryGrant", 
    "url": "http://www.rfbr.ru/rffi/ru/project_search/o_78483"
  }
]
 

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/grant.5464257'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/grant.5464257'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/grant.5464257'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/grant.5464257'


 

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

104 TRIPLES      17 PREDICATES      94 URIs      88 LITERALS      3 BLANK NODES

Subject Predicate Object
1 sg:grant.5464257 schema:about anzsrc-for:2201
2 schema:description link has been studied between all the different types of canonical bases Gelfand-Zeitlin for finite-dimensional irreducible representations of the quantum algebra Uq (su (3)). It was clearly shown that the coefficients of such a connection, called the Weyl coefficients are equal (up to a few simple factors) q-coefficients Cancer (or q-6j symbols) quantum algebra Uq (su (2)). He developed the theory of Clebsch-Gordan coefficients (Wigner) for the quantum algebra Uq (u (3)). The canonical solution to the problem of multiplicity in the tensor product of irreducible finite-dimensional representations of the algebra u (3), proposed Biedenharnom, Lauck and Hecht and implemented in computer codes Draerom and Akiyama, was generalized to the case of quantum algebra Uq (u (3)). The method of projection operators had obtained an analytical formula for the special ( "seed") Uq (u (3)) - Wigner coefficients. This result can be used which can be used in the circuit-Draera Akiyama for other Wigner coefficients normalized for the conventional algebra U (3) and for q-deformed algebra Uq (su (3)). They were calculated and tabulated all isoscalar factors such as <(22) '(22) || (lm)> q with unit multiplicity. Found a new two-parameter deformation of the universal enveloping algebra U (g [u]) for the Lie polynomial current algebra g [u] over any simple finite-dimensional complex Lie algebra g. It is shown that such a quantum Hopf algebra can be seen as quantization of U (g [u]) in the direction of classical r-matrix, which is the sum of the simplest rational and trigonometric solutions of the Yang-Baxter classical equation, depending on the parameters. Studied classical limit elliptic algebra Aq, p (sl2) and its variant limiting Ax, h (sl2). The corresponding Lie algebra is the central extension of the algebra sl2-valued generalized (doubly) - periodic functions. Classic elliptic and trigonometric solutions of the classical Yang-Baxter equation are interpreted in terms of Lie formalism Semenov-Tyan-Shan. Presenting geometric realization of the category of finite-dimensional representations of simple Lie algebra with a tensor structure defined monodromies solutions KZ equation (kvazitenzornoy Drinfeld category). It is proved that this kvazitenzornaya category equivalent to the category of factoring modules over the ring
3 schema:endDate 1996-12-31T00:00:00Z
4 schema:funder https://www.grid.ac/institutes/grid.452899.b
5 schema:identifier N42e6b706560d44e3b758177f232df55f
6 Nbea84a2bdd2e495e928d7c920ddafd31
7 schema:inLanguage ru
8 schema:keywords Akiyama
9 Biedenharnom
10 Classic elliptic
11 Clebsch-Gordan coefficients
12 Hecht
13 Lauck
14 Lie algebra
15 Lie formalism Semenov-Tyan
16 Lie polynomial current algebra g
17 METHODS
18 New group-theoretic methods
19 SL2
20 Shan
21 UQ
22 Weyl coefficients
23 Wigner
24 Wigner coefficients
25 Yang-Baxter classical equation
26 algebra
27 algebra U
28 analytical formula
29 axes
30 canonical bases Gelfand-Zeitlin
31 canonical solution
32 cases
33 categories
34 central extension
35 circuit-Draera Akiyama
36 classical Yang-Baxter equation
37 classical limit
38 coefficient
39 coefficients Cancer
40 computer codes Draerom
41 connection
42 conventional algebra U
43 deformed algebra Uq
44 different types
45 direction
46 elliptic algebra Aq
47 factoring modules
48 few simple factors
49 finite-dimensional irreducible representations
50 finite-dimensional representations
51 geometric realization
52 irreducible finite-dimensional representations
53 isoscalar factors
54 kvazitenzornaya category
55 kvazitenzornoy Drinfeld category
56 link
57 matrix
58 monodromies solutions KZ equation
59 multiplicity
60 other Wigner coefficients
61 parameters
62 periodic functions
63 problem
64 projection operators
65 q-6j symbols
66 quantization
67 quantum Hopf algebra
68 quantum algebra Uq
69 quantum physics
70 results
71 ring
72 seeds
73 simple Lie algebras
74 simple finite-dimensional complex Lie algebra g.
75 sum
76 tensor product
77 tensor structure
78 terms
79 theory
80 trigonometric solutions
81 two-parameter deformation
82 unit multiplicity
83 variants
84 schema:name New group-theoretic methods in quantum physics
85 schema:sameAs https://app.dimensions.ai/details/grant/grant.5464257
86 schema:sdDatePublished 2019-03-07T12:53
87 schema:sdLicense https://scigraph.springernature.com/explorer/license/
88 schema:sdPublisher Nfd8f7ef324124cdfb90c34dbbf92e0c3
89 schema:startDate 1996-01-01T00:00:00Z
90 schema:url http://www.rfbr.ru/rffi/ru/project_search/o_78483
91 sgo:license sg:explorer/license/
92 sgo:sdDataset grants
93 rdf:type schema:MonetaryGrant
94 N42e6b706560d44e3b758177f232df55f schema:name dimensions_id
95 schema:value 5464257
96 rdf:type schema:PropertyValue
97 Nbea84a2bdd2e495e928d7c920ddafd31 schema:name rfbr_id
98 schema:value 96-01-01421
99 rdf:type schema:PropertyValue
100 Nfd8f7ef324124cdfb90c34dbbf92e0c3 schema:name Springer Nature - SN SciGraph project
101 rdf:type schema:Organization
102 anzsrc-for:2201 schema:inDefinedTermSet anzsrc-for:
103 rdf:type schema:DefinedTerm
104 https://www.grid.ac/institutes/grid.452899.b schema:Organization
 




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


...