Fine gradings and their Weyl groups for twisted Heisenberg Lie superalgebras

TL;DR

This paper classifies fine gradings and determines Weyl groups for twisted Heisenberg Lie superalgebras, extending understanding of their algebraic structure and symmetries.

Contribution

It introduces the classification of fine gradings and computes Weyl groups for twisted Heisenberg superalgebras, a novel extension of existing algebraic theory.

Findings

Classification of fine gradings up to equivalence

Determination of Weyl groups for these gradings

Extension of structure theory for twisted Heisenberg superalgebras

Abstract

In this paper we define the so-called twisted Heisenberg superalgebras over the complex number field by adding derivations to Heisenberg superalgebras. We classify the fine gradings up to equivalence on twisted Heisenberg superalgebras and determine the Weyl groups of those gradings.