Derivations of the finite-dimensional special odd Hamiltonian superalgebras

TL;DR

This paper completely determines the derivation algebras of finite-dimensional special odd Hamiltonian superalgebras of Cartan-type over fields with characteristic p > 3, including their outer derivations.

Contribution

It provides the first complete description of derivations for these superalgebras, including restricted, simple, nonrestricted, and non-simple cases.

Findings

Derived the derivations of negative Z-degree for all cases.

Determined the derivation algebras and outer derivation algebras.

Extended results to nonrestricted and non-simple superalgebras.

Abstract

The aim is to determine the derivations of the three series of finite-dimensional Z-graded Lie superalgebras of Cartan-type over a field of characteristic p > 3, called the special odd Hamiltonian superalgebras. To that end we first determine the derivations of negative Z-degree for the restricted and simple special odd Hamiltonian superalgebras by means of weight space decompositions. Then the results are used to determine the derivations of negative Z-degree for the nonrestricted and non-simple special odd Hamiltonian superalgebras. Finally the derivation algebras and the outer derivation algebras of those Lie superalgebras are completely determined.