Examples of tensor categories
\textit{P. Deligne} [Grothendieck Festschrift, Vol. II, Prog. Math. 87, 111- 195 (1990; Zbl 0727.14010)] characterized those \(k\)-linear tensor categories of the form \(\text{Rep}(G)\) for some proalgebraic group scheme \(G\) over a field \(k\) of characteristic zero. Using quotients (by ideals) of subcategories of categories of representations of algebraic Chevalley groups, the authors show that this characterization does not work for \(k\) of positive characteristic. They describe how to correct Deligne's result in this case. They also construct interesting examples of semisimple braided tensor categories as quotients of categories of representations of Hopf algebras (quantum groups) over the ring of integers in a cyclotomic field.
categories of representations of algebraic Chevalley groups
categories of representations of Hopf algebras
scientific article; zbMATH DE number 220752
scientific article