Jordan-Lie inner ideals of finite dimensional associative algebras

TL;DR

This paper investigates Jordan-Lie inner ideals in finite dimensional associative algebras and their Lie algebra counterparts, establishing Levi decompositions and classifying minimal ideals generated by idempotents.

Contribution

It provides a classification of Jordan-Lie inner ideals satisfying minimality conditions and demonstrates their generation by pairs of idempotents.

Findings

Jordan-Lie inner ideals admit Levi decompositions.

Minimal Jordan-Lie inner ideals are generated by pairs of idempotents.

Classification of these ideals under certain conditions.

Abstract

We study Jordan-Lie inner ideals of finite dimensional associative algebras and the corresponding Lie algebras and prove that they admit Levi decompositions. Moreover, we classify Jordan-Lie inner ideals satisfying a certain minimality condition and show that they are generated by pairs of idempotents.