On Lie $p$-algebras of cohomological dimension one

TL;DR

This paper proves that Lie p-algebras with cohomological dimension one are necessarily one-dimensional, providing a classification result and discussing related algebraic questions.

Contribution

It establishes a fundamental classification result for Lie p-algebras of cohomological dimension one, showing they are necessarily one-dimensional.

Findings

Lie p-algebras of cohomological dimension one are one-dimensional

Discussion of related algebraic questions

Provides a classification result for this class of algebras

Abstract

We prove that a Lie $p$-algebra of cohomological dimension one is one-dimensional, and discuss related questions.