Simple transitive 2-representations of left cell 2-subcategories of projective functors for star algebras

In this article, we study simple transitive 2-representations of certain 2-subcategories of the 2-category of projective functors over a star algebra. We show that in the simplest case, which is associated to the Dynkin type A 2 , simple transitive 2-representations are classified by cell 2-represen...

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Bibliographic Details
Published in:Communications in algebra 2019-03, Vol.47 (3), p.1222-1237
Main Author: Zimmermann, Jakob
Format: Article
Language:English
Subjects:
2-representation theory
Cell 2-representations
projective functors
Representations
simple transitive 2-representations
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Summary:In this article, we study simple transitive 2-representations of certain 2-subcategories of the 2-category of projective functors over a star algebra. We show that in the simplest case, which is associated to the Dynkin type A 2 , simple transitive 2-representations are classified by cell 2-representations. In the general case we conjecture that there exist many simple transitive 2-representations which are not cell 2-representations and provide some evidence for our conjecture.
ISSN:0092-7872
1532-4125
1532-4125
DOI:10.1080/00927872.2018.1501578