Projective dimension and commuting variety of a reductive Lie algebra
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866917990166953984 |
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| author | Charbonnel, Jean-Yves |
| author_facet | Charbonnel, Jean-Yves |
| contents | The commuting variety of a reductive Lie algebra $\mathfrak{g}$ is the underlying variety of a well defined subscheme of $\mathfrak{g}\times\mathfrak{g}$. In this note, it is proved that this scheme is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime ideal. As a matter of fact, this theorem results from a so called Property (P) for a simple Lie algebra. This property says that some cohomology complexes are exact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_12942 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Projective dimension and commuting variety of a reductive Lie algebra Charbonnel, Jean-Yves Algebraic Geometry Representation Theory The commuting variety of a reductive Lie algebra $\mathfrak{g}$ is the underlying variety of a well defined subscheme of $\mathfrak{g}\times\mathfrak{g}$. In this note, it is proved that this scheme is normal and Cohen-Macaulay. In particular, its ideal of definition is a prime ideal. As a matter of fact, this theorem results from a so called Property (P) for a simple Lie algebra. This property says that some cohomology complexes are exact. |
| title | Projective dimension and commuting variety of a reductive Lie algebra |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2006.12942 |