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 JordanH{\"o}lder 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 $2$KacMoody algebras.
Original language  English 

Pages (fromto)  76237644 
Journal  Transactions of the American Mathematical Society 
Volume  368 
Issue number  11 
Early online date  22 Dec 2015 
DOIs  
Publication status  Published  Nov 2016 
Keywords
 math.RT
 math.CT
Profiles

Vanessa Miemietz
 School of Mathematics  Associate Professor in Pure Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research