Coherence Isomorphisms for a Hopf Category View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2001

AUTHORS

Volodymyr Lyubashenko

ABSTRACT

Crane and Frenkel proposed a notion of a Hopf category in [1]. It was motivated by Lusztig’s approach to quantum groups—his theory of canonical bases. In particular, Lusztig obtains braided deformations of universal enveloping algebras for some nilpotent Lie algebras together with canonical bases of these braided Hopf algebras [2–4]. The elements of the canonical basis are identified with certain objects of equivariant derived categories, contained in semisimple abelian subcategories of semisimple complexes. Conjectural properties of these categories were collected into a system of axioms of a Hopf category, equipped with functors of multiplication and comultiplication, isomorphisms of associativity, coassociativity and coherence which satisfy four equations [1]. Crane and Frenkel gave an example of a Hopf category resembling the semisimple category encountered in Lusztig’s theory corresponding to one-dimensional Lie algebra —nilpotent subalgebra of . The mathematical framework and some further examples of Hopf categories were provided by Neuchl [5]. More... »

PAGES

283-294

References to SciGraph publications

Book

TITLE

Noncommutative Structures in Mathematics and Physics

ISBN

978-0-7923-6999-8
978-94-010-0836-5

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-94-010-0836-5_22

DOI

http://dx.doi.org/10.1007/978-94-010-0836-5_22

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1000833077


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