Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations

Marco MacKaay; Volodymyr Mazorchuk; Vanessa Miemietz; Xiaoting Zhang

doi:10.1017/S1474748018000555

Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations

Marco MacKaay, Volodymyr Mazorchuk, Vanessa Miemietz, Xiaoting Zhang

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

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

7 Citations (SciVal)

20 Downloads (Pure)

Abstract

The main result of this paper establishes a bijection between the set of equivalence classes of simple transitive 2-representations with a fixed apex of a fiat 2-category and the set of equivalence classes of faithful simple transitive 2-representations of the fiat 2-subquotient of associated with a diagonal-cell in. As an application, we classify simple transitive 2-representations of various categories of Soergel bimodules, in particular, completing the classification in types and.

Original language	English
Pages (from-to)	1793-1829
Number of pages	37
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	19
Issue number	6
Early online date	4 Dec 2018
DOIs	https://doi.org/10.1017/S1474748018000555
Publication status	Published - Nov 2020

Keywords

2-category
coalgebra 1-morphism
cotensor product
simple transitive 2-representation

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10.1017/S1474748018000555

Accepted manuscriptAccepted author manuscript, 450 KB

https://arxiv.org/abs/1802.02078

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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KW - 2-category

KW - coalgebra 1-morphism

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KW - simple transitive 2-representation

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ER -

Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations

Abstract

Keywords

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Vanessa Miemietz

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