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

Author

Listed:
  • Senlin Zhang

    (School of Mathematics, Southeast University, Nanjing 210096, China)

  • Shuanhong Wang

    (Shing-Tung Yau Center, School of Mathematics, Southeast University, Nanjing 210096, China)

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.

Suggested Citation

  • Senlin Zhang & Shuanhong Wang, 2022. "Group-Graded By-Product Construction and Group Double Centralizer Properties," Mathematics, MDPI, vol. 10(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2943-:d:888791
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