Compatible left-symmetric algebraic structures on high rank Witt and Virasoro algebras

TL;DR

This paper classifies all graded and non-graded compatible left-symmetric algebraic structures on high rank Witt and Virasoro algebras, providing a comprehensive understanding of their algebraic compatibility.

Contribution

It offers a complete classification of compatible left-symmetric structures on high rank Witt and Virasoro algebras, including non-graded cases under certain conditions.

Findings

Classified all graded compatible left-symmetric structures on high rank Witt algebras

Classified all non-graded compatible structures satisfying a minor condition

Classified graded compatible structures on high rank Virasoro algebras

Abstract

We classify all graded compatible left-symmetric algebraic structures on high rank Witt algebras, and classify all non-graded ones satisfying a minor condition. Furthermore, graded compatible left-symmetric algebraic structures on high rank Virasoro algebras are also classified.