2020/10/31 by Ilya Shapiro · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Differential (mechanical device) #Homotopy and Cohomology in Algebraic Topology #Hopf algebra #Mathematics #Physics #Pure mathematics #math.KT #msc:16E35 #msc:16T05 #msc:18G90 #msc:19D55
paper · pdf · doi:10.3842/sigma.2021.026
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
openalex created_date 2020/10/15 · arxiv created 2021/03/17 · openalex publication_date 2021/03/17 · arxiv updated 2021/03/18 · openalex updated_date 2026/08/05
We examine the cyclic homology of the monoidal category of modules over a finite dimensional Hopf algebra, motivated by the need to demonstrate that there is a difference between the recently introduced mixed anti-Yetter-Drinfeld contramodules and the usual stable anti-Yetter-Drinfeld contramodules. Namely, we show that Sweedler's Hopf algebra provides an example where mixed complexes in the category of stable anti-Yetter-Drinfeld contramodules (previously studied) are not equivalent, as differential graded categories to the category of mixed anti-Yetter-Drinfeld contramodules (recently introduced).