Covariant Bimodules Over Monoidal Hom-Hopf Algebras
Quantum Algebra
2019-05-28 v2 Mathematical Physics
math.MP
Abstract
Covariant Hom-bimodules are introduced and the structure theory of them in the Hom-setting is studied in a detailed way. The category of bicovariant Hom-bimodules is proved to be a (pre)braided monoidal category and its structure theory is also provided in coordinate form. The notion of Hom-Yetter-Drinfel'd modules is presented and it is shown that the category of Hom-Yetter-Drinfel'd modules is a (pre)braided tensor category as well. As one of the main results, a (pre)braided monoidal equivalence between these tensor categories is verified, which extends the fundamental theorem of Hom-Hopf modules.
Keywords
Cite
@article{arxiv.1404.1296,
title = {Covariant Bimodules Over Monoidal Hom-Hopf Algebras},
author = {Serkan Karaçuha},
journal= {arXiv preprint arXiv:1404.1296},
year = {2019}
}
Comments
40 pages, errors and typos corrected. Structure theory of covariant Hom-bimodules in coordinate form added