Higher Frobenius-Schur Indicators for Semisimple Hopf Algebras in Positive Characteristic  

作　　者：Zhihua Wang Gongxiang Liu Libin Li 

机构地区：[1]Department of Mathematics,Taizhou University,Taizhou,Jiangsu 225300,China [2]Department of Mathematics,Nanjing University,Nanjing 210093,China [3]School of Mathematical Science,Yangzhou University,Yangzhou,Jiangsu 225002,China

出　　处：《Algebra Colloquium》2024年第4期675-688,共14页代数集刊（英文版）

基　　金：National Natural Science Foundation of China(Grant No.12271243);National Natural Science Foundation of China(Grant No.12371041).

摘　　要：Let H be a semisimple Hopf algebra over an algebraically closed field Ik of characteristic p>dimk(H)^(1/2).We show that the antipode S of H satisfies the equality S^(2)(h)=uhu^(-1),where h e H,u=S(A_((2))A_((1))and A is a nonzero integral of H.The formula of s^(2) enables us to define higher Frobenius-Schur indicators for the Hopf algebra H.This generalizes the notion of higher Frobenius-Schur indicators from the case of characteristic O to the case of characteristic p>dimk(H)^(1/2).These indicators defined here share some properties with the ones defined over a field of characteristic 0.In particular,all these indicators are gauge invariants for the tensor category Rep(H)of finite-dimensional representations of H.

关 键 词：s2-formula Frobenius-Schur indicator gauge invariant 

分 类 号：O151[理学—数学]