Finite generation of Lie derived powers of associative algebras

TL;DR

This paper proves that for associative algebras generated by finitely many nilpotent elements over a field with characteristic not 2, all their Lie derived powers are finitely generated Lie algebras.

Contribution

It establishes the finite generation of Lie derived powers for a broad class of associative algebras generated by nilpotent elements, extending understanding of their Lie algebra structure.

Findings

All Lie derived powers are finitely generated Lie algebras.

Applicable to associative algebras over fields with characteristic not 2.

Provides new insights into the structure of Lie derived powers.

Abstract

Let $A$ be an associative algebra over a field of characteristic $\neq 2$ that is generated by a finite collection of nilpotent elements. We prove that all Lie derived powers of $A$ are finitely generated Lie algebras.