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Radford $[(m,k),m]$-biproduct Theorem for Generalized Hom-crossed Products

Botong Gai, Shuanhong Wang

Abstract

In this paper, we mainly provide a new approache to construct Hom-Hopf algebras. For this, we introduce and study the notion of a left $(m,k)$-Hom-crossed product structure as a generalization of $k$-Hom-smash product structure. Then one combines this $(m,k)$-Hom-crossed product structure and a left $m$-Hom-smash coproduct structure to build Radford $[(m,k),m]$-biproduct theorem. Finally, we study Hom admissible mappping system to characterize this Radford $[(m,k),m]$-biproduct structure.

Radford $[(m,k),m]$-biproduct Theorem for Generalized Hom-crossed Products

Abstract

In this paper, we mainly provide a new approache to construct Hom-Hopf algebras. For this, we introduce and study the notion of a left -Hom-crossed product structure as a generalization of -Hom-smash product structure. Then one combines this -Hom-crossed product structure and a left -Hom-smash coproduct structure to build Radford -biproduct theorem. Finally, we study Hom admissible mappping system to characterize this Radford -biproduct structure.
Paper Structure (10 sections, 54 equations, 1 table)

This paper contains 10 sections, 54 equations, 1 table.

Table of Contents

  1. Introduction
  2. 1. Preliminaries
  3. 2. $(m,k)$-Hom-crossed products
  4. 3. Radford $[(m,k),m]$-biproducts
  5. 4. Hom admissible mappping system
  6. Acknowledgements