Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld\n double of a Hom-Hopf algebra

2014/03/27 by Abdenacer Makhlouf, Florin Panaite, Makhlouf, Abdenacer +1 · 1 citation
Chemistry · Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1403.7077

openalex publication_date 2014/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the Hom-analogue of the L-R-smash product and use it to define\nthe Hom-analogue of the diagonal crossed product. When H is a finite\ndimensional Hom-Hopf algebra with bijective antipode and bijective structure\nmap, we define the Drinfeld double of H; its algebra structure is a\nHom-diagonal crossed product and it has all expected properties, namely it is\nquasitriangular and modules over it coincide with left-right Yetter-Drinfeld\nmodules over H.\n

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• BiHom-L-R-smash biproduct and BiHom-Yetter-Drinfel'd-Long category

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