DJKM algebras I: Their Universal Central Extension

TL;DR

This paper explicitly describes the universal central extension of a specific infinite-dimensional Lie algebra related to integrable systems, providing generators and relations for a deeper algebraic understanding.

Contribution

It offers a detailed presentation of the universal central extension of a particular Lie algebra associated with Landau-Lifshitz integrable systems, expanding the algebraic framework.

Findings

Explicit generators and relations for the universal central extension.

Enhanced understanding of the algebraic structure related to integrable systems.

Foundation for further algebraic and integrable systems research.

Abstract

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, $\mathfrak g\otimes \mathbb C[t,t^{-1},u|u^2=(t^2-b^2)(t^2-c^2)]$, appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of integrable systems arising from Landau-Lifshitz differential equation.