Transposed Poisson Structure on the Kantor double of Virasoro-like algebra

2025/12/15 by Lin, Jie, Liu, Chengyu, Jiang, Jingjing
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2512.12961

Abstract

Following Kantor's procedure, we construct the Kantor double of Virasoro-like algebra and delve into the study of transposed Poisson structures on this Lie superalgebra. Our findings establish that it lacks non-trivial 1/2 -derivations, and therefore, it does not exhibit a non-trivial transposed Poisson algebra structure.

Citations

• Quasi-derivations of Witt and related algebras
• (Transposed) Poisson algebra structures on null-filiform associative algebras
• On the simple transposed Poisson algebras and Jordan superalgebras
• Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
• Jet modules for the centerless Virasoro-like algebra

Related

• On the simple transposed Poisson algebras and Jordan superalgebras
• Transposed Poisson structures on the extended Schrödinger-Virasoro and the original deformative Schrödinger-Virasoro algebras
• Transposed Poisson structures on Virasoro-type algebras
• Transposed Poisson superalgebra
• Transposed Poisson structures on the q-analog Virasoro-like algebras and q-Quantum Torus Lie algebras