On Isotypic Decompositions for Non-Semisimple Hopf Algebras

Vincent Koppen*, Ehud Meir, Christoph Schweigert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study the isotypic decomposition of the regular module of a finite-dimensional Hopf algebra over an algebraically closed field of characteristic zero. For a semisimple Hopf algebra, the idempotents realizing the isotypic decomposition can be explicitly expressed in terms of characters and the Haar integral. In this paper we investigate Hopf algebras with the Chevalley property, which are not necessarily semisimple. We find explicit expressions for idempotents in terms of Hopf-algebraic data, where the Haar integral is replaced by the regular character of the dual Hopf algebra. For a large class of Hopf algebras, these are shown to form a complete set of orthogonal idempotents. We give an example which illustrates that the Chevalley property is crucial.

Original languageEnglish
JournalAlgebras and Representation Theory
Early online date31 Jan 2021
DOIs
Publication statusE-pub ahead of print - 31 Jan 2021

Keywords

  • Non-semisimple Hopf algebras

Fingerprint

Dive into the research topics of 'On Isotypic Decompositions for Non-Semisimple Hopf Algebras'. Together they form a unique fingerprint.

Cite this