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 , we construct an associative enveloping algebra and prove that is equivalent to the category of left -modules. Under a Maschke-type condition on the group component, we show that short exact sequences split on the -side, while the obstruction to full splitting is described by cocycles and identified with . We also derive a spectral sequence with consequences for splitting and non-semisimplicity.
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}
}