On Cohomology group of current Lie algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909384756428800 |
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| author | García-Delgado, R. |
| author_facet | García-Delgado, R. |
| contents | In this work we state a result that relates the cohomology groups of a Lie algebra $\mathfrak{g}$ and a current Lie algebra $\mathfrak{g} \otimes \mathcal{S}$, by means of a short exact sequence -- similar to the universal coefficients theorem for modules -- where $\mathcal{S}$ is a finite dimensional, commutative and associative algebra with unit over a field $\mathbb{F}$. Although this result can be applied to any Lie algebra, we determine the cohomology group of $\mathfrak{g} \otimes \mathcal{S}$, where $\mathfrak{g}$ is a semisimple Lie algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00553 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Cohomology group of current Lie algebras García-Delgado, R. Rings and Algebras 17B05, 17B56, 17B60 (Primary) 17B10, 17B20 (Secondary) In this work we state a result that relates the cohomology groups of a Lie algebra $\mathfrak{g}$ and a current Lie algebra $\mathfrak{g} \otimes \mathcal{S}$, by means of a short exact sequence -- similar to the universal coefficients theorem for modules -- where $\mathcal{S}$ is a finite dimensional, commutative and associative algebra with unit over a field $\mathbb{F}$. Although this result can be applied to any Lie algebra, we determine the cohomology group of $\mathfrak{g} \otimes \mathcal{S}$, where $\mathfrak{g}$ is a semisimple Lie algebra. |
| title | On Cohomology group of current Lie algebras |
| topic | Rings and Algebras 17B05, 17B56, 17B60 (Primary) 17B10, 17B20 (Secondary) |
| url | https://arxiv.org/abs/2401.00553 |