Year: 2025
Type: article
Abstract: In this work we state a result that relates the cohomology groups of a Lie algebra $\frak g$ and a current Lie algebra $\frak g \otimes \mathcal{S}$, by means of a short exact sequence similar to the universal coefficients theorem for modules, where $\mathcal{S}$ is a finite dimensional, commutative and associative algebra with unit over a field $\Bbb F$. Using this result we determine the cohomology group of $\frak g \otimes \mathcal{S}$ where $\frak g$ is a semisimple Lie algebra.
Author: Rosendo Garcia Delgado
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4412516666