The Drinfel'd codouble constuction for monoidal Hom-Hopf algebra

2020/02/12 by Dongdong Yan, Yan, Dongdong, Shuanhong Wang +1
Mathematics · #16T05 #16W30 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2002.04842

openalex publication_date 2020/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (H, β) be a monoidal Hom-Hopf algebra with the bijective antipode S, In this paper, we mainly construct the Drinfel'd codouble T(H)=(H^op⊗ H^*, β⊗ β^*-1) and \widehatT(H)=( H^*⊗ H^op, β^*-1⊗ β) in the setting of monoidal Hom-Hopf algebras. Then we prove both T(H) and \widehatT(H) are coquasitriangular. Finally, we discuss the relation between Drinfel'd codouble and Heisenberg double in the setting of monoidal Hom-Hopf algebras, which is a generalization of the part results in \citeL94.

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