Transitive 2-representations of finitary 2-categories

By Volodymyr Mazorchuk, Vanessa Miemietz. 2014

79 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6741c52fce1714af19924188e5d1e4b6a5b1fb29

Citations in the corpus

• Endomorphisms of cell 2-representations (2012, unknown): “In particular, the main result of [MM4] asserts that in this cases cell 2 -representations exhaust all simple transitive 2 -representations.”