Pyramids and 2-representations

2017/05/09 by Volodymyr Mazorchuk, Mazorchuk, Volodymyr, Vanessa Miemietz +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1705.03174

openalex publication_date 2017/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• 2-Kac-Moody algebras
• 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

Related

• Simple transitive 2-representations of some 2-categories of projective functors
• 2-categories of symmetric bimodules and their 2-representations
• Simple transitive 2-representations for two non-fiat 2-categories of projective functors
• On Simple Transitive 2-representations of Bimodules over the Dual Numbers
• Simple transitive 2-representations of Soergel bimodules in type B₂