Transitive $2$-representations of finitary $2$-categories
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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-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.References
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Additional Information
- Volodymyr Mazorchuk
- Affiliation: Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden
- MR Author ID: 353912
- Email: mazor@math.uu.se
- Vanessa Miemietz
- Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
- Email: v.miemietz@uea.ac.uk
- Received by editor(s): May 14, 2014
- Received by editor(s) in revised form: September 18, 2014
- Published electronically: December 22, 2015
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 7623-7644
- MSC (2010): Primary 18D05; Secondary 16D20, 17B10, 16G10
- DOI: https://doi.org/10.1090/tran/6583
- MathSciNet review: 3546777