Universal central extensions of direct limits of Lie superalgebras

TL;DR

This paper proves that the universal central extension of a direct limit of perfect Lie superalgebras is the direct limit of their universal central extensions, and applies this to infinite rank Lie superalgebras.

Contribution

It establishes a fundamental property of universal central extensions in the context of direct limits of Lie superalgebras, extending known results.

Findings

Universal central extension of a direct limit equals the direct limit of extensions

Application to infinite rank Lie superalgebras

Provides explicit descriptions of extensions for certain classes

Abstract

We show that the universal central extension of a direct limit of perfect Lie superalgebras L_i is (isomorphic to) the direct limit of the universal central extensions of L_i. As an application we describe the universal central extensions of some infinite rank Lie superalgebras.