Group-Graded By-Product Construction and Group Double Centralizer Properties

Senlin Zhang and Shuanhong Wang ()
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Senlin Zhang: School of Mathematics, Southeast University, Nanjing 210096, China
Shuanhong Wang: Shing-Tung Yau Center, School of Mathematics, Southeast University, Nanjing 210096, China

Mathematics, 2022, vol. 10, issue 16, 1-24

Abstract: For a group π with unit e , we introduce and study the notion of a π -graded Hopf algebra. Then we introduce and construct a new braided monoidal category H H e YD π over a π -graded Hopf algebra H . We introduce the notion of a π -double centralizer property and investigate this property by studying a braided π -graded Hopf algebra U ( g l n ( V ) ) ⋉ π H , where V is an n -dimensional vector space in H H e YD π and U ( g l n ( V ) ) is the braided universal enveloping algebra of g l n ( V ) which is not the usual Hopf algebra. Finally, some examples and special cases are given.

Keywords: group-graded Hopf algebras; symmetric braided categories; group Yetter–Drinfeld categories; group double centralizer properties (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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