Transposed Poisson superalgebra structures on twisted $N=1$ Block–Lie superalgebra

Anqi Huang, Yun Gao and Jiancai Sun

Vol. 335 (2025), No. 1, 119–161

DOI: 10.2140/pjm.2025.335.119

Abstract

We investigate the transposed Poisson superalgebra structures on the twisted $N=1$ Block–Lie superalgebra $\mathcal{𝒮}(p,q)$, where $p$ and $q$ are arbitrary complex numbers. We obtain that $\mathcal{𝒮}(p,q)$ admits only trivial transposed Poisson superalgebra structure for $q\ne 0$ or $p\notin \mathbb{Z}$, while $\mathcal{𝒮}(p,q)$ has nontrivial transposed Poisson superalgebra structures for $q=0$ and $p\in \mathbb{Z}$, which are nonisomorphic with respect to $p\in \mathbb{Z}$.

Keywords

twisted $N=1$ Block–Lie superalgebra, transposed Poisson superalgebra, $\frac{1}{2}$-superderivation

Mathematical Subject Classification

Primary: 17B05, 17B40, 17B68

Milestones

Received: 17 May 2024

Revised: 25 November 2024

Accepted: 23 February 2025

Published: 8 April 2025