Finite symmetric tensor categories with the Chevalley property in characteristic 2

2019/04/16 by Etingof, Pavel, Gelaki, Shlomo
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1904.07576

Abstract

We prove an analog of Deligne's theorem for finite symmetric tensor categories C with the Chevalley property over an algebraically closed field k of characteristic 2. Namely, we prove that every such category C admits a symmetric fiber functor to the symmetric tensor category D of representations of the triangular Hopf algebra (k[\dd]/(\dd²),1\ot 1 + \dd\ot \dd). Equivalently, we prove that there exists a unique finite group scheme G in D such that C is symmetric tensor equivalent to \Rep_D(G). Finally, we compute the group H²_{\rm inv}(A,K) of equivalence classes of twists for the group algebra K[A] of a finite abelian p-group A over an arbitrary field K of characteristic p>0, and the Sweedler cohomology groups Hⁱ_\rmSw(O(A),K), i≥ 1, of the function algebra O(A) of A.

Related

• Finite symmetric integral tensor categories with the Chevalley property
• The classification of finite-dimensional triangular Hopf algebras over an algebraically closed field of characteristic 0
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