Transposed Poisson structures on the extended Schrödinger-Virasoro and the original deformative Schrödinger-Virasoro algebras

Z. Kh. Shermatova

Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 2, pp. 1385-1399

Résumé

We compute $\frac{1}{2}$-derivations on the extended Schrödinger-Virasoro algebras and the original deformative Schrödinger-Virasoro algebras. The extended Schrödinger-Virasoro algebras have neither nontrivial $\frac{1}{2}$-derivations nor nontrivial transposed Poisson algebra structures. We demonstrate that the original deformative Schrödinger-Virasoro algebras have nontrivial $\frac{1}{2}$-derivations, indicating that they possess nontrivial transposed Poisson structures.

Détail

Keywords: Lie algebra, extended Schrödinger-Virasoro algebra, original deformative Schrödinger-Virasoro algebra, transposed Poisson algebra, $\frac 1 2$-derivation.

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