The Drinfel'd Double versus the Heisenberg Double for Hom-Hopf Algebras

2014/09/25 by Daowei Lu, Lu, Daowei, Shuanhong Wang +1 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1409.7152

openalex publication_date 2014/09/25 · arxiv created 2015/03/23 · arxiv updated 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (A,α) be a finite-dimensional Hom-Hopf algebra. In this paper we mainly construct the Drinfel'd double D(A)=(A^op\bowtie A^∗,α⊗(α^-1)^∗) in the setting of Hom-Hopf algebras by two ways, one of which generalizes Majid's bicrossproduct for Hopf algebras (see \citeM2) and another one is to introduce the notion of dual pairs of of Hom-Hopf algebras. Then we study the relation between the Drinfel'd double D(A) and Heisenberg double H(A)=A# A^*, generalizing the main result in \citeLu. Especially, the examples given in the paper are not obtained from the usual Hopf algebras.

Citations

• Module Hom-algebras

Cited by

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

Related

• Drinfel'd double for monoidal Hom-Hopf algebras
• The Drinfel'd codouble constuction for monoidal Hom-Hopf algebra
• Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra
• Hom-Lie-Hopf algebras
• Duality Theorem and Drinfeld Double in Braided Tensor Categories