The character algebra for module categories over Hopf algebras

2018/08/14 by Bortolussi, Noelia, Mombelli, Martín
#18D10 #18D20 #Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1808.04810

Abstract

Given a finite dimensional Hopf algebra H and an exact indecomposable module category M over Rep(H), we explicitly compute the adjoint algebra A_M as an object in the category of Yetter-Drinfeld modules over H, and the space of class functions CF(M) associated to M, as introduced by K. Shimizu [ Further results on the structure of (Co)ends in fintite tensor categories, preprint arXiv:1801.02493]. We use our construction to describe these algebras when H is a group algebra and a dual group algebra. This result allows us to compute the adjoint algebra for certain group-theoretical fusion categories.

Related

• Finite tensor categories
• Module categories over pointed Hopf algebras
• Module categories over finite pointed tensor categories
• On Lie Algebras in the Category of Yetter-Drinfeld Modules
• The monoidal center and the character algebra