The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917099946901504 |
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| author | Bouarroudj, Sofiane Ehret, Quentin Makhlouf, Abdenacer Shyntas, Nurtas |
| author_facet | Bouarroudj, Sofiane Ehret, Quentin Makhlouf, Abdenacer Shyntas, Nurtas |
| contents | The main goal of this paper is to introduce the notion of restricted Lie-Rinehart superalgebra over a field of characteristic $p>2$, motivated by a generalization of Hochschild's lemma to the super setting. We extend Schauenburg's proof of Hochschild's lemma to Lie-Rinehart superalgebras and we prove a superized version that serves as a foundation for our construction. Building upon this, we define restricted Lie-Rinehart superalgebras, investigate their representations, construct the semi-direct product with a restricted module, and provide several examples. Finally, we construct the corresponding universal enveloping algebra and show that this algebra satisfies the expected universal property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18372 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras Bouarroudj, Sofiane Ehret, Quentin Makhlouf, Abdenacer Shyntas, Nurtas Representation Theory 17B50, 17B60, 17A70, 16W25 The main goal of this paper is to introduce the notion of restricted Lie-Rinehart superalgebra over a field of characteristic $p>2$, motivated by a generalization of Hochschild's lemma to the super setting. We extend Schauenburg's proof of Hochschild's lemma to Lie-Rinehart superalgebras and we prove a superized version that serves as a foundation for our construction. Building upon this, we define restricted Lie-Rinehart superalgebras, investigate their representations, construct the semi-direct product with a restricted module, and provide several examples. Finally, we construct the corresponding universal enveloping algebra and show that this algebra satisfies the expected universal property. |
| title | The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras |
| topic | Representation Theory 17B50, 17B60, 17A70, 16W25 |
| url | https://arxiv.org/abs/2511.18372 |