On finite-dimensional subalgebras of derivation Lie algebras

TL;DR

This paper investigates the structure of finite-dimensional subalgebras within derivation Lie algebras, providing descriptions of injective mappings from Lie algebras to derivation algebras over commutative associative algebras.

Contribution

It offers new characterizations of embeddings of Lie algebras into derivation Lie algebras over commutative algebras.

Findings

Descriptions of injections from Lie algebras to derivation Lie algebras.

Structural insights into finite-dimensional subalgebras of derivation Lie algebras.

Framework for understanding Lie algebra embeddings in derivation contexts.

Abstract

Let $\mathbb{K}$ be a field, $R$ be an associative and commutative $\mathbb{K}$-algebra and $L$ be a Lie algebra over $\mathbb{K}$. We give some descriptions of injections from $L$ to Lie algebra of $\mathbb{K}$-derivations of $R$ in the terms of $L$.