Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 17 (2021), 026, 10 pages      arXiv:2010.02768      https://doi.org/10.3842/SIGMA.2021.026

Mixed vs Stable Anti-Yetter-Drinfeld Contramodules

Ilya Shapiro
Department of Mathematics and Statistics, University of Windsor, 401 Sunset Avenue, Windsor, Ontario N9B 3P4, Canada

Received November 09, 2020, in final form March 04, 2021; Published online March 17, 2021

Abstract
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).

Key words: Hopf algebras; homological algebra; Taft algebras.

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