Maschke functors, semisimple functors and separable functors of the second kind. Applications

2001/12/20 by S. Caenepeel, G. Militaru, Caenepeel, S. +1 · 1 citation
Mathematics · #16B50 #16W30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:16B50 #msc:16W30

paper · pdf · doi:10.48550/arxiv.math/0112226

23 pages

arxiv created 2001/12/20 · openalex publication_date 2001/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce separable functors of the second kind (or H-separable functors) and H-Maschke functors. H-separable functors are generalizations of separable functors. Various necessary and sufficient conditions for a functor to be H-separable or H-Maschke, in terms of generalized (co)Casimir elements (integrals, in the case of Hopf algebras), are given. An H-separable functor is always H-Maschke, but the converse holds in particular situations. A special role will be played by Frobenius functors and their relations to H-separability. Our concepts are applied to modules, comodules, entwined modules, quantum Yetter-Drinfeld modules, relative Hopf modules.

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