Representations and categorical realization of Hom-quasi-Hopf algebras

doi:10.1007/s11464-015-0460-4

Front. Math. China

2015, Vol. 10

Issue (6) : 1263-1281 https://doi.org/10.1007/s11464-015-0460-4

RESEARCH ARTICLE

Representations and categorical realization of Hom-quasi-Hopf algebras

Yongsheng CHENG^1,^*(

),Xiufu ZHANG²

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

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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.

Keywords Monoidal category Hom-coassociative 2-coalgebra Hom-quasi-Hopf algebra

Corresponding Author(s): Yongsheng CHENG

Issue Date: 12 October 2015

Cite this article:

Yongsheng CHENG,Xiufu ZHANG. Representations and categorical realization of Hom-quasi-Hopf algebras[J]. Front. Math. China, 2015, 10(6): 1263-1281.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-015-0460-4
https://academic.hep.com.cn/fmc/EN/Y2015/V10/I6/1263

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