Simple transitive $2$-representations and Drinfeld center for some finitary $2$-categories

Abstract

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.

References in corpus (6)

• 2-Kac-Moody algebras
• Derived equivalences for symmetric groups and sl\_2-categorification
• Gabriel 2-Quivers for Finitary 2-Categories
• Transitive 2-representations of finitary 2-categories
• Duflo involutions for 2-categories associated to tree quivers
• Isotypic faithful $2$-representations of $\mathcal{J}$-simple fiat $2$-categories

Cited by in corpus (8)

• Simple transitive 2-representations for two non-fiat 2-categories of projective functors
• Bimodules over uniformly oriented A_n quivers with radical square zero
• Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
• Characterisation and applications of $\mathbb{k}$-split bimodules
• Multisemigroups with multiplicities and complete ordered semi-rings
• Pyramids and 2-representations
• Sub-bimodules of the identity bimodule for cyclic quivers
• Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n