Transitive 2-representations of finitary 2-categories

Volodymyr Mazorchuk; Vanessa Miemietz

doi:10.1090/tran/6583

Transitive 2-representations of finitary 2-categories

Volodymyr Mazorchuk, Vanessa Miemietz

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

41 Citations (Scopus)

24 Downloads (Pure)

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 language	English
Pages (from-to)	7623-7644
Number of pages	22
Journal	Transactions of the American Mathematical Society
Volume	368
Issue number	11
Early online date	22 Dec 2015
DOIs	https://doi.org/10.1090/tran/6583
Publication status	Published - Nov 2016

Keywords

math.RT
math.CT

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10.1090/tran/6583

transitnewAccepted author manuscript, 390 KB

Vanessa Miemietz
- V.Miemietzuea.acuk
- School of Engineering, Mathematics and Physics - Professor in Pure Mathematics
- Algebra, Number Theory, Logic, and Representations (ANTLR) - Member
Person: Research Group Member, Academic, Teaching & Research

Cite this

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AB - 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.

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Transitive 2-representations of finitary 2-categories

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Vanessa Miemietz

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