Monoidal Category Approach to Dual Hom-quasi-Hopf Algebras

CHENG Yong-sheng, LIU Guo-jing

doi:10.13371/j.cnki.chin.q.j.m.2015.02.009

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 2: 218 - 226

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.02.009

Monoidal Category Approach to Dual Hom-quasi-Hopf Algebras

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1. School of Mathematics and Statistics, Institute of Contemporary Mathematics, Henan University2. People's Liberation Army of China,95129 Troops

CHENG Yong-sheng(1973-), male, native of Lankao, Henan, an associate professor of Henan University, Ph.D., engages in Lie theory.

Received date: 2013-06-08

Online published: 2020-11-23

Supported by

Supported by the National Natural Science Foundation of China(11047030,11171055)； Supported by the Grant from China Scholarship Council(2011841026)；

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Abstract

In this paper, we categorify a Hom-associative algebra by imposing the Homassociative law up to some isomorphisms on the multiplication map and requiring that these isomorphisms satisfy the Pentagon axiom, and obtain a 2-Hom-associative algebra. On the other hand, we introduce the dual Hom-quasi-Hopf algebra and show that any dual Homquasi-Hopf algebras can be viewed as a 2-Hom-associative algebra.

Key words： Monoidal category; 2-Hom-associative algebra; dual Hom-quasi-Hopf algebra

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CHENG Yong-sheng, LIU Guo-jing . Monoidal Category Approach to Dual Hom-quasi-Hopf Algebras[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(2) : 218 -226 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.02.009

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