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- W4367694628 abstract "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." @default.
- W4367694628 created "2023-05-03" @default.
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- W4367694628 date "2023-05-01" @default.
- W4367694628 modified "2023-09-27" @default.
- W4367694628 title "Transposed Poisson structures on the Lie algebra of upper triangular matrices" @default.
- W4367694628 doi "https://doi.org/10.48550/arxiv.2305.00727" @default.
- W4367694628 hasPublicationYear "2023" @default.
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