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Title: Yetter-Drinfeld modules for Hom-bialgebras

The aim of this paper is to define and study Yetter-Drinfeld modules over Hom-bialgebras, a generalized version of bialgebras obtained by modifying the algebra and coalgebra structures by a homomorphism. Yetter-Drinfeld modules over a Hom-bialgebra with bijective structure map provide solutions of the Hom-Yang-Baxter equation. The category H/HYD of Yetter-Drinfeld modules with bijective structure maps over a Hom-bialgebra H with bijective structure map can be organized, in two different ways, as a quasi-braided pre-tensor category. If H is quasitriangular (respectively, coquasitriangular) the first (respectively, second) quasi-braided pre-tensor category H/HYD contains, as a quasi-braided pre-tensor subcategory, the category of modules (respectively, comodules) with bijective structure maps over H.
Authors:
 [1] ;  [2]
  1. Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, rue des frères Lumière, F-68093 Mulhouse (France)
  2. Institute of Mathematics of the Romanian Academy, PO-Box 1-764, RO-014700 Bucharest (Romania)
Publication Date:
OSTI Identifier:
22251712
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 1; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; EQUATIONS; MAPS; MATHEMATICAL SOLUTIONS; TENSORS