English

Cohomological Maschke's Theorem for Generalized Digroups

Representation Theory 2026-05-05 v1

Abstract

We study Maschke-type phenomena in the representation theory of generalized digroups. For a generalized digroup DD, we construct an associative enveloping algebra ADA_D and prove that Rep(D)Rep(D) is equivalent to the category of left ADA_D-modules. Under a Maschke-type condition on the group component, we show that short exact sequences split on the ρ\rho-side, while the obstruction to full splitting is described by cocycles and identified with ExtRep(D)1(Q,W)Ext^1_{Rep(D)}(Q,W). We also derive a spectral sequence with consequences for splitting and non-semisimplicity.

Keywords

Cite

@article{arxiv.2605.01215,
  title  = {Cohomological Maschke's Theorem for Generalized Digroups},
  author = {José Gregorio Rodríguez-Nieto and Olga Patricia Salazar-Díaz and Andrés Sarrazola-Alzate and Raúl Velásquez},
  journal= {arXiv preprint arXiv:2605.01215},
  year   = {2026}
}
R2 v1 2026-07-01T12:46:14.949Z