Omni-representations of Leibniz algebras
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916171308072960 |
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| author | Liu, Zhangju Sheng, Yunhe |
| author_facet | Liu, Zhangju Sheng, Yunhe |
| contents | In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the omni-cohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili cohomology groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02809 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Omni-representations of Leibniz algebras Liu, Zhangju Sheng, Yunhe Rings and Algebras Representation Theory In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the omni-cohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili cohomology groups. |
| title | Omni-representations of Leibniz algebras |
| topic | Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2304.02809 |