Transitive 2-representations of finitary 2-categories

Volodymyr Mazorchuk, Vanessa Miemietz

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27 Citations (Scopus)
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Abstract

In this article, we define and study the class of simple transitive $2$-representations of finitary $2$-categories. We prove a weak version of the classical Jordan-H{\"o}lder Theorem where the weak composition subquotients are given by simple transitive $2$-representations. For a large class of finitary $2$-categories we prove that simple transitive $2$-representations are exhausted by cell $2$-representations. Finally, we show that this large class contains finitary quotients of $2$-Kac-Moody algebras.
Original languageEnglish
Pages (from-to)7623-7644
JournalTransactions of the American Mathematical Society
Volume368
Issue number11
Early online date22 Dec 2015
DOIs
Publication statusPublished - Nov 2016

Keywords

  • math.RT
  • math.CT

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