Cohomological Maschke's Theorem for Generalized Digroups
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911640051515392 |
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| author | Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl |
| author_facet | Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl |
| contents | 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 $ρ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01215 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Cohomological Maschke's Theorem for Generalized Digroups Rodríguez-Nieto, José Gregorio Salazar-Díaz, Olga Patricia Sarrazola-Alzate, Andrés Velásquez, Raúl Representation Theory 20M10, 20C99, 16D90, 18G15 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 $ρ$-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. |
| title | Cohomological Maschke's Theorem for Generalized Digroups |
| topic | Representation Theory 20M10, 20C99, 16D90, 18G15 |
| url | https://arxiv.org/abs/2605.01215 |