Can I read Finite symmetric integral tensor categories with the Chevalley property on EtoBox?

Finite symmetric integral tensor categories with the Chevalley property by Etingof, Pavel; Gelaki, Shlomo is a scholarly article available to read on EtoBox.

What is Finite symmetric integral tensor categories with the Chevalley property about?

We prove that every finite symmetric integral tensor category $\mathcal{C}$ with the Chevalley property over an algebraically closed field $k$ of characteristic $p>2$ admits a symmetric fiber functor to $\text{sVec}$. This proves Ostrik's conjecture \cite[Conjecture 1.3]{o} in this case. Equivalently, we prove that there exists a unique finite supergroup scheme $\mathcal{G}$ over $k$ and a grouplike element $\epsilon\in k[\mathcal{G}]$ of order $\le 2$, whose action by conjugation on $\mathcal{G}$ coincides with the parity automorphism of $\mathcal{G}$, such that $\mathcal{C}$ is symmetric tensor equivalent to $\Rep(\mathcal{G},\epsilon)$. In particular, when $\mathcal{C}$ is unipotent, the functor lands in $\Vect$, so $\mathcal{C}$ is symmetric tensor equivalent to $\Rep(U)$ for a unique finite unipotent group scheme $U$ over $k$. We apply our result and the results of \cite{g} to classify certain finite dimensional triangular Hopf algebras with the Chevalley property over $k$ (e.g., local), in group scheme-theoretical terms. Finally, we compute the Sweedler cohomology of restricted enveloping algebras over an algebraically closed field $k$ of characteristic $p>0$, classify associ

Author

Etingof, Pavel; Gelaki, Shlomo

Published

2019

Language

EN