Symmetric super-biderivations of the Hamiltonian Lie superalgebra $H(m, n;\underline{t})$

Abstract

Let $H$ denote the Hamiltonian Lie superalgebra $H(m, n;\underline{t})$ over a field of characteristic $p\ge 3$, which has a finite $\mathbb{Z}$-graded structure. In this paper, we take the canonical torus $T_H$ of $H$, which is the abelian subalgebra of $H$. By the decomposition of the weight space of $H$ with respect to $T_H$, we show the action of symmetric super-biderivation on the elements of $T_H$ and the generators of $H$. Moreover, we prove that each symmetric super-biderivation of $H$ is zero. As applications, the supercommutative post-Lie superalgebra structures on $H$ are described.