Schrodinger-Virasoro Lie $H$-pseudoalgebras

TL;DR

This paper introduces and classifies Schrödinger-Virasoro Lie H-pseudoalgebras, expanding the understanding of their structure and related Leibniz pseudoalgebras, which are significant in mathematical physics.

Contribution

It provides a comprehensive classification of Schrödinger-Virasoro Lie H-pseudoalgebras and all Leibniz H-pseudoalgebras of rank two, filling a gap in the mathematical theory.

Findings

Classification of Schrödinger-Virasoro Lie H-pseudoalgebras

Determination of all Leibniz H-pseudoalgebras of rank two

Enhanced understanding of conformal algebra structures

Abstract

Schrodinger-Virasoro Lie algebras are annihilation algebras of Lie conformal algebras of rank three, which are widely studied by mathematicians and physicists. Conformal algebras are also called H-pseudoalgebras, where H = k[s] is the polynomial algebra over a field k. In this article, we introduce and classify Schrodinger-Virasoro Lie H-pseudoalgebras. Meanwhile we also determine all Leibniz H-pseudoalgebras of rank two.