Transposed Poisson structures on the Lie algebra of upper triangular matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910387222347776 |
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| author | Kaygorodov, Ivan Khrypchenko, Mykola |
| author_facet | Kaygorodov, Ivan Khrypchenko, Mykola |
| contents | We describe transposed Poisson structures on the upper triangular matrix Lie algebra $T_n(F)$, $n>1$, over a field $F$ of characteristic zero. We prove that, for $n>2$, any such structure is either of Poisson type or the orthogonal sum of a fixed non-Poisson structure with a structure of Poisson type, and for $n=2$, there is one more class of transposed Poisson structures on $T_n(F)$. We also show that, up to isomorphism, the full matrix Lie algebra $M_n(F)$ admits only one non-trivial transposed Poisson structure, and it is of Poisson type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Transposed Poisson structures on the Lie algebra of upper triangular matrices Kaygorodov, Ivan Khrypchenko, Mykola Rings and Algebras We describe transposed Poisson structures on the upper triangular matrix Lie algebra $T_n(F)$, $n>1$, over a field $F$ of characteristic zero. We prove that, for $n>2$, any such structure is either of Poisson type or the orthogonal sum of a fixed non-Poisson structure with a structure of Poisson type, and for $n=2$, there is one more class of transposed Poisson structures on $T_n(F)$. We also show that, up to isomorphism, the full matrix Lie algebra $M_n(F)$ admits only one non-trivial transposed Poisson structure, and it is of Poisson type. |
| title | Transposed Poisson structures on the Lie algebra of upper triangular matrices |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2305.00727 |