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Transitive $ 2$-representations of finitary $ 2$-categories


Authors: Volodymyr Mazorchuk and Vanessa Miemietz
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
Published electronically: December 22, 2015
MathSciNet review: 3546777
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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.


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Additional Information

Volodymyr Mazorchuk
Affiliation: Department of Mathematics, Uppsala University, Box 480, 751 06, Uppsala, Sweden
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

DOI: https://doi.org/10.1090/tran/6583
Received by editor(s): May 14, 2014
Received by editor(s) in revised form: September 18, 2014
Published electronically: December 22, 2015
Article copyright: © Copyright 2015 American Mathematical Society