Transitive 2-representations of finitary 2-categories

Mazorchuk, Volodymyr and Miemietz, Vanessa (2016) Transitive 2-representations of finitary 2-categories. Transactions of the American Mathematical Society, 368 (11). pp. 7623-7644. ISSN 1088-6850

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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.

Item Type:	Article
Additional Information:	Revised version to appear in Transactions of the AMS
Uncontrolled Keywords:	math.rt,math.ct
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Logic & Number Theory
Depositing User:	Pure Connector
Date Deposited:	08 Feb 2016 14:00
Last Modified:	11 Nov 2024 00:40
URI:	https://ueaeprints.uea.ac.uk/id/eprint/56988
DOI:	10.1090/tran/6583

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