English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We prove that every finite symmetric integral tensor category $\mathcal{C}$with the Chevalley property over an algebraically closed field $k$ ofcharacteristic $p>2$ admits a symmetric fiber functor to $\text{sVec}$. Thisproves 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 parityautomorphism of $\mathcal{G}$, such that $\mathcal{C}$ is symmetric tensorequivalent to $\Rep(\mathcal{G},\epsilon)$. In particular, when $\mathcal{C}$is unipotent, the functor lands in $\Vect$, so $\mathcal{C}$ is symmetrictensor 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 certainfinite dimensional triangular Hopf algebras with the Chevalley property over$k$ (e.g., local), in group scheme-theoretical terms. Finally, we compute theSweedler cohomology of restricted enveloping algebras over an algebraicallyclosed field $k$ of characteristic $p>0$, classify associators for their duals,and study finite dimensional (not necessarily triangular) local quasi-Hopfalgebras and finite (not necessarily symmetric) unipotent tensor categoriesover an algebraically closed field $k$ of characteristic $p>0$.  The appendix by K. Coulembier and P. Etingof gives another proof of the aboveclassification results using the recent paper \cite{Co}, and, more generally,shows that the maximal Tannakian and super-Tannakian subcategory of a symmetrictensor category over a field of characteristic $\ne 2$ is always a Serresubcategory.

Finite symmetric integral tensor categories with the Chevalley property