Generators of Supersymmetric Classical $W$-algebras

TL;DR

This paper constructs generators for supersymmetric classical W-algebras associated with certain Lie superalgebras using a matrix determinant method, advancing algebraic understanding in supersymmetry.

Contribution

It introduces a new method to generate supersymmetric classical W-algebras via the row determinant of a specific matrix related to the Lie superalgebra and its nilpotent element.

Findings

Explicit generators for supersymmetric classical W-algebras obtained

Matrix determinant method applied to Lie superalgebras of type sl and osp

Provides a systematic approach for algebraic structure analysis

Abstract

Let $\mathfrak{g}$ be a Lie superalgebra of type $\mathfrak{sl}$ or $\mathfrak{osp}$ with an odd principal nilpotent element $f$. We consider a matrix $\mathcal{A}_{\mathfrak{g},f}$ determined by $\mathfrak{g}$ and $f$ and find a generating set of the supersymmetric classical $W$-algebra $\mathcal{W}(\bar{\mathfrak{g}},f)$ using the row determinant of $\mathcal{A}_{\mathfrak{g},f}$.