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arXiv · 2605.01215

Cohomological Maschke's Theorem for Generalized Digroups

José Gregorio Rodríguez-Nieto·Olga Patricia Salazar-Díaz·Andrés Sarrazola-Alzate·Raúl Velásquez
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Abstract

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

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José Gregorio Rodríguez-Nieto, Olga Patricia Salazar-Díaz, Andrés Sarrazola-Alzate, Raúl Velásquez. 2026-05-02. Cohomological Maschke's Theorem for Generalized Digroups. https://arxiv.org/abs/2605.01215

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