Locally loop algebras and locally affine Lie algebras

TL;DR

This paper introduces and classifies a new class of infinite-rank Lie algebras called locally affine and locally loop algebras, which generalize affine Lie algebras by extending their structure to a local, infinite-dimensional setting.

Contribution

It defines, explores, and classifies locally affine and locally loop Lie algebras, extending the theory of affine Lie algebras to a local, infinite-rank context.

Findings

Classification of locally affine Lie algebras

Identification of their centerless cores as local loop algebras

Extension of affine Lie algebra theory to infinite rank

Abstract

We investigate a new class of Lie algebras, which are tame locally extended affine Lie algebras of nullity 1. It is an infinite-rank analog of affine Lie algebras, and their centerless cores are a local version of loop algebras. Such algebras are called locally affine Lie algebras and locally loop algebras. We classify both of them.