Universal coverings of Lie tori (A finite presentation)

TL;DR

This paper provides a finite presentation for the universal covering algebra of certain Lie tori, expanding the understanding of their structure using root-graded Lie algebra theorems.

Contribution

It introduces a unified method to derive finite presentations for universal coverings of centerless Lie tori of specific types, excluding A, C, and BC.

Findings

Finite presentation for universal coverings of Lie tori of type X not equal to A, C, BC.

Unified approach applicable across multiple Lie torus types.

Enhanced structural understanding of Lie tori universal coverings.

Abstract

Using the well-known recognition and structural theorem(s) for root-graded Lie algebras and their universal coverings, we give a finite presentation for the universal covering algebra of a centerless Lie torus of type $X\not=A,C,BC$. We follow a unified approach for the types under consideration.