Super $w_{\infty}$ 3-algebra

TL;DR

This paper explores the structure of the super $w_{inity}$ 3-algebra, deriving it from the super high-order Virasoro 3-algebra through scaling limits and defining a compatible super Nambu-Poisson bracket.

Contribution

It introduces the super $w_{inity}$ 3-algebra, establishes its satisfaction of the fundamental identity, and presents its realization via a super Nambu-Poisson bracket.

Findings

Super $w_{inity}$ 3-algebra satisfies the generalized fundamental identity.

A super Nambu-Poisson bracket is defined with key algebraic properties.

Realization of the super $w_{inity}$ 3-algebra using the super Nambu-Poisson bracket.

Abstract

We investigate the super high-order Virasoro 3-algebra. By applying the appropriate scaling limits on the generators, we obtain the super $w_{\infty}$ 3-algebra which satisfies the generalized fundamental identity condition. We also define a super Nambu-Poisson bracket which satisfies the generalized skewsymmetry, Leibniz rule and fundamental identity. By means of this super Nambu-Poisson bracket, the realization of the super $w_{\infty}$ 3-algebra is presented.