Transitive 2-representations of finitary 2-categories

Mazorchuk, Volodymyr; Miemietz, Vanessa

doi:10.1090/tran/6583

Transitive $2$-representations of finitary $2$-categories
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Trans. Amer. Math. Soc. 368 (2016), 7623-7644 Request permission

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-Hölder 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.

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