Frontiers of Mathematics in China >

2015 , Vol. 10 >Issue 6: 1263 - 1281

DOI: https://doi.org/10.1007/s11464-015-0460-4

RESEARCH ARTICLE

Representations and categorical realization of Hom-quasi-Hopf algebras

  • Yongsheng CHENG , 1 ,
  • Xiufu ZHANG 2
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  • 1. School of Mathematics and Statistics and Institute of Contemporary Mathematics, Henan University, Kaifeng 475004, China
  • 2. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, China

Received date: 05 Jul 2014

Accepted date: 05 Feb 2015

Published date: 12 Oct 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

We give a monoidal category approach to Hom-coassociative coalgebra by imposing the Hom-coassociative law up to some isomorphisms on the comultiplication map and requiring that these isomorphisms satisfy the copentagon axiom and obtain a Hom-coassociative 2-coalgebra, which is a 2- category. Second, we characterize Hom-bialgebras in terms of their categories of modules. Finally, we give a categorical realization of Hom-quasi-Hopf algebras using Hom-coassociative 2-coalgebra.

Key words： Monoidal category; Hom-coassociative 2-coalgebra; Hom-quasi-Hopf algebra

Cite this article

Yongsheng CHENG , Xiufu ZHANG . Representations and categorical realization of Hom-quasi-Hopf algebras[J]. Frontiers of Mathematics in China, 2015 , 10(6) : 1263 -1281 . DOI: 10.1007/s11464-015-0460-4

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