Extensions between finite-dimensional simple modules over a generalized current Lie algebra

TL;DR

This paper computes the first extension groups between finite-dimensional simple modules over generalized current Lie algebras, encompassing loop Lie algebras and multivariable cases, advancing understanding of their module category structure.

Contribution

It provides explicit calculations of extension groups for simple modules over generalized current Lie algebras, a significant step in understanding their representation theory.

Findings

Calculated first extension groups for simple modules

Included cases of loop and multivariable current Lie algebras

Enhanced understanding of module category structure

Abstract

We calculate the first extension groups for finite-dimensional simple modules over an arbitrary generalized current Lie algebra, which includes the case of loop Lie algebras and their multivariable analogs.