2018/03/24 by Ivan Kobyzev, Kobyzev, Ivan, Ilya Shapiro +2 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Hopf algebra (16T05) #K-Theory and Homology (math.KT) #Monoidal category (18D10) #Quantum Algebra (math.QA) #Rings, Modules, and Algebras #abelian and additive category (18E05) #cyclic homology (19D55) #math.CT #math.KT #math.QA
paper · pdf · doi:10.48550/arxiv.1803.09194
Final version, to appear in Applied Categorical Structures
openalex publication_date 2018/03/24 · arxiv created 2018/09/24 · arxiv updated 2018/09/26 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We apply categorical machinery to the problem of defining cyclic cohomology with coefficients in two particular cases, namely quasi-Hopf algebras and Hopf algebroids. In the case of the former, no definition was thus far available in the literature, and while a definition exists for the latter, we feel that our approach demystifies the seemingly arbitrary formulas present there. This paper emphasizes the importance of working with a biclosed monoidal category in order to obtain natural coefficients for a cyclic theory that are analogous to the stable anti-Yetter-Drinfeld contramodules for Hopf algebras.