Skew-symmetric super-biderivations of the special odd Hamiltonian superalgebra SHO(n, n; t)

Abstract: This paper aims to study the skew-symmetric super-biderivations of the special odd Hamiltonian superalgebra SHO(n, n; t). Let HO denote the odd Hamiltonian Lie superalgebra HO(n, n; t) and SHO the special odd Hamiltonian Lie superalgebra SHO(n, n; t) over a field of characteristic p > 2.Utilizing the abelian subalgebra TSHO and the weight space decomposition of HO with respect to TSHO , we show the action of a skew-symmetric super-biderivation on the elements of TSHO and some specific elements of SHO. Moreover, we prove that all skew-symmetric super-biderivations of SHO are inner.