2019/03/31 by Kenichi Shimizu, Shimizu, Kenichi · 3 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1904.00376
openalex publication_date 2019/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let C be a finite tensor category, and let M be an exact left C-module category. The relative Serre functor of M is an endofunctor \mathbbS on M together with a natural isomorphism \underlineHom(M, N)^* ≅ \underlineHom(N, \mathbbS(M)) for M, N ∈ M, where \underlineHom is the internal Hom functor of M. In this paper, we discuss the case where C and M are the category of modules over a finite-dimensional Hopf algebra H and the category of modules over an H-comodule algebra L, respectively. We give an explicit description of the relative Serre functor of M and its twisted module structure in terms of the Frobenius structure of L. We also study pivotal structures on M and give some concrete examples.