Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Higher Frobenius-Schur indicators for semisimple Hopf algebras in positive characteristic (2112.15264v2)

Published 31 Dec 2021 in math.RT

Abstract: Let $H$ be a semisimple Hopf algebra over an algebraically closed field $\mathbbm{k}$ of characteristic $p>\dim_{\mathbbm{k}}(H){1/2}$. We show that the antipode $S$ of $H$ satisfies the equality $S2(h)=\mathbf{u}h\mathbf{u}{-1}$, where $h\in H$, $\mathbf{u}=S(\Lambda_{(2)})\Lambda_{(1)}$ and $\Lambda$ is a nonzero integral of $H$. The formula of $S2$ enables us to define higher Frobenius-Schur indicators for the Hopf algebra $H$. This generalizes the notions of higher Frobenius-Schur indicators from the case of characteristic 0 to the case of characteristic $p>\dim_{\mathbbm{k}}(H){1/2}$. These indicators defined here share some properties with the ones defined over a field of characteristic 0. Especially, all these indicators are gauge invariants for the tensor category Rep$(H)$ of finite dimensional representations of $H$.

Summary

We haven't generated a summary for this paper yet.