English

Transitive 2-representations of finitary 2-categories

Representation Theory 2016-12-30 v3 Category Theory

Abstract

In this article, we define and study the class of simple transitive 22-representations of finitary 22-categories. We prove a weak version of the classical Jordan-H\"older Theorem where the weak composition subquotients are given by simple transitive 22-representations. For a large class of finitary 22-categories we prove that simple transitive 22-representations are exhausted by cell 22-representations. Finally, we show that this large class contains finitary quotients of 22-Kac-Moody algebras.

Keywords

Cite

@article{arxiv.1404.7589,
  title  = {Transitive 2-representations of finitary 2-categories},
  author = {Volodymyr Mazorchuk and Vanessa Miemietz},
  journal= {arXiv preprint arXiv:1404.7589},
  year   = {2016}
}

Comments

revised version to appear in Transactions of the AMS, proof of Proposition 22 corrected

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