Generalized Crossed Products and L-R Smash&nbsp;Products of Multiplier Hopf Algebras

ZHAO Li-hui, WANG Cai-hong

doi:10.13371/j.cnki.chin.q.j.m.2014.02.019

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 2: 283 - 291

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.02.019

Generalized Crossed Products and L-R Smash Products of Multiplier Hopf Algebras

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1. School of Mathematics and Statistics, Henan University of Science and Technology 2. Department of Mathematics, Zhejiang University 3. College of Mathematics and Information Science, Henan Polytechnic University

ZHAO Li-hui(1979-), female, native of Luoyang, Henan, a lecturer of Henan University of Science and Technology, Ph.D., engages in noncommutative algebra; WANG Cai-hong(1980-), female, native of Zhengzhou, Henan, a lecturer of Henan Polytechnic University, Ph.D., engages in noncommutative algebra.

Received date: 2012-12-19

Online published: 2023-04-10

Supported by

Supported by the Scientific Research Foundation for Doctoral Scientists of Henan University of Science and Technology(09001303)； Supported by the National Natural Science Foundation of China(11101128)

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Abstract

In this paper we generalize the notions of crossed products and L-R smash products in the context of multiplier Hopf algebras. We use comodule algebras to define generalized diagonal crossed products, L-R smash products, two-sided smash products and two-sided crossed products and prove that they are all associative algebras. Then we show the isomorphic relations of them.

Key words： multiplier Hopf algebra; diagonal crossed product; L-R smash product; two-sided smash product; two-sided crossed product

Cite this article

ZHAO Li-hui, WANG Cai-hong . Generalized Crossed Products and L-R Smash Products of Multiplier Hopf Algebras[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(2) : 283 -291 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.02.019

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