Transitive 2-representations of Finitary 2-categories
نویسندگان
چکیده
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.
منابع مشابه
Simple Transitive 2-representations and Drinfeld Center for Some Finitary 2-categories
We classify all simple transitive 2-representations for two classes of finitary 2-categories associated with tree path algebras and also for one class of fiat 2-categories associated with truncated polynomial rings. Additionally, we compute the Drinfeld centers for all these 2-categories.
متن کاملMorita Theory for Finitary 2-categories
We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for 2-categories of Soergel bimodules.
متن کاملCell 2-representations of finitary 2-categories
We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations inspired by KazhdanLusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do no...
متن کاملIsotypic Faithful 2-representations of J -simple Fiat 2-categories
We introduce the class of isotypic 2-representations for finitary 2categories and the notion of inflation of 2-representations. Under some natural assumptions we show that isotypic 2-representations are equivalent to inflations of cell 2-representations.
متن کاملar X iv : 1 70 5 . 03 17 4 v 1 [ m at h . R T ] 9 M ay 2 01 7 PYRAMIDS AND 2 - REPRESENTATIONS
We describe a diagrammatic procedure which lifts strict monoidal actions from additive categories to categories of complexes avoiding any use of direct sums. As an application, we prove that every simple transitive 2-representation of the 2-category of projective bimodules over a finite dimensional algebra is equivalent to a cell 2-representation.
متن کامل