Simple transitive 2-representations for two non-fiat 2-categories of projective functors

Abstract

We show that any simple transitive $2$-representation of the $2$-ca\-te\-go\-ry of projective endofunctors for the quiver algebra of $\Bbbk(\xymatrix{\bullet\ar[r]&\bullet})$ and for the quiver algebra of $\Bbbk(\xymatrix{\bullet\ar[r]\ar@/^/@{.}[rr]&\bullet\ar[r]&\bullet})$ is equivalent to a cell $2$-representation.

23 pages

References in corpus (6)

• 2-Kac-Moody algebras
• Categorification of the braid groups
• Simple transitive $2$-representations and Drinfeld center for some finitary $2$-categories
• Transitive 2-representations of finitary 2-categories
• Duflo involutions for 2-categories associated to tree quivers
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Cited by in corpus (6)

• Analogues of centralizer subalgebras for fiat 2-categories and their 2-representations
• Characterisation and applications of $\mathbb{k}$-split bimodules
• Pyramids and 2-representations
• Sub-bimodules of the identity bimodule for cyclic quivers
• Counting Quasi-Idempotent Irreducible Integral Matrices
• Fiat categorification of the symmetric inverse semigroup IS_n and the semigroup F^*_n