Duflo involutions for 2-categories associated to tree quivers

Abstract

Motivated by the definition of Duflo involution for fiat $2$-categories, we define certain analogues of Duflo involution for arbitrary finitary $2$-categories and show that such Duflo involutions exist for two classes of finitary $2$-categories associated with tree path algebras. Additionally, we describe the quiver for the algebra underlying the principal $2$-representation for these two classes of finitary $2$-categories.

References in corpus (3)

• 2-Kac-Moody algebras
• Transitive 2-representations of finitary 2-categories
• Isotypic faithful $2$-representations of $\mathcal{J}$-simple fiat $2$-categories

Cited by in corpus (6)

• Simple transitive 2-representations via (co)algebra 1-morphisms
• Simple transitive $2$-representations and Drinfeld center for some finitary $2$-categories
• Simple transitive 2-representations for two non-fiat 2-categories of projective functors
• Bimodules over uniformly oriented A_n quivers with radical square zero
• Multisemigroups with multiplicities and complete ordered semi-rings
• Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n