## Finite-dimensional special contact superalgebras of odd type over a field of prime characteristic

### Volume 155 / 2019

#### Abstract

We consider an infinite family of finite-dimensional Lie superalgebras over a field $\mathbb{F}$ of characteristic $p \gt 2$, special contact Lie superalgebras of odd type, denoted by $\mathfrak{sm}_{\lambda}(n;\underline{N})$ and parameterized by $\lambda\in \mathbb{F}$. The second derived subalgebra of $\mathfrak{sm}_{\lambda}(n;\underline{N})$ is proved to be simple by finding a linear spanning set of $\mathfrak{sm}_{\lambda}(n;\underline{N})$. In the process a direct sum decomposition of $\mathfrak{sm}_{\lambda}(n;\underline{N})$ is given in terms of its first or second derived subalgebras. Moreover, dimension formulas for these Lie superalgebras are established and comparison with the known simple Lie superalgebras of Cartan type shows that the second derived subalgebras of the Lie superalgebras $\mathfrak{sm}_{\lambda}(n;\underline{N})$ constitute a new infinite family of finite-dimensional simple Lie superalgebras.