Revista Matemática Iberoamericana

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Published online first: 2019-11-25
DOI: 10.4171/rmi/1133

Pyramids and 2-representations

Volodymyr Mazorchuk[1], Vanessa Miemietz[2] and Xiaoting Zhang[3]

(1) Uppsala Universitet, Sweden
(2) University of East Anglia, Norwich, UK
(3) Uppsala Universitet, Sweden

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.

Keywords: 2-category, 2-representation, simple transitive 2-representation, projective bimodule, finite dimensional algebra

Mazorchuk Volodymyr, Miemietz Vanessa, Zhang Xiaoting: Pyramids and 2-representations. Rev. Mat. Iberoam. Electronically published on November 25, 2019. doi: 10.4171/rmi/1133 (to appear in print)