Revista Matemática Iberoamericana
Full-Text PDF (303 KB) | List online-first RMI articles | RMI summary
Pyramids and 2-representationsVolodymyr Mazorchuk, Vanessa Miemietz and Xiaoting Zhang (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)