Blocks inequivalent to their Frobenius twists

David John Benson, Radha Kessar

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

Let k be an algebraically closed field of characteristic p. We give a general method for producing examples of blocks B of finite group algebras that are not Morita equivalent as k-algebras to the Frobenius twist B(P). Our method produces non-nilpotent blocks having one simple module and elementary abelian defect group. These also provide the first known examples of blocks where there is a perfect isotypy at the level of ordinary characters with all the signs positive, but no derived equivalence between the blocks. We do not know of any examples of blocks B that are not Morita equivalent to the second Frobenius twist B(P-2).

Original languageEnglish
Pages (from-to)588-599
Number of pages12
JournalJournal of Algebra
Volume315
Issue number2
Early online date1 May 2007
DOIs
Publication statusPublished - 15 Sep 2007

Keywords

  • blocks
  • Group algebras
  • one simple module
  • representation

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