Chinese Quarterly Journal of Mathematics ›› 2015, Vol. 30 ›› Issue (2): 218-226.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.009

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Monoidal Category Approach to Dual Hom-quasi-Hopf Algebras

  

  1. 1. School of Mathematics and Statistics, Institute of Contemporary Mathematics, Henan University2. People's Liberation Army of China,95129 Troops
  • Received:2013-06-08 Online:2015-06-30 Published:2020-11-23
  • About author:CHENG Yong-sheng(1973-), male, native of Lankao, Henan, an associate professor of Henan University, Ph.D., engages in Lie theory.
  • 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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