2019/09/21 by Gelaki, Shlomo
#FOS: Mathematics #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1909.10908
Let k be an algebraically closed field of characteristic 0 or p>2. Let G be an affine supergroup scheme over k. We classify the indecomposable exact module categories over the tensor category \rm sCoh\rm f(G) of (coherent sheaves of) finite dimensional O(G)-supermodules in terms of (H,Ψ)-equivariant coherent sheaves on G. We deduce from it the classification of indecomposable \em geometrical module categories over \sRep(G). When G is finite, this yields the classification of \em all indecomposable exact module categories over the finite tensor category \sRep(G). In particular, we obtain a classification of twists for the supergroup algebra kG of a finite supergroup scheme G, and then combine it with \cite[Corollary 4.1]EG3 to classify finite dimensional triangular Hopf algebras with the Chevalley property over k.