Engel condition on enveloping algebras of lie superalgebras

TL;DR

This paper investigates conditions under which the enveloping algebras of Lie superalgebras over fields of characteristic p are bounded Lie Engel, extending understanding of their algebraic structure.

Contribution

It establishes criteria for when the enveloping algebra of a Lie superalgebra is bounded Lie Engel in various characteristic settings.

Findings

u(L) or U(L) is bounded Lie Engel under specific conditions

Results depend on the characteristic of the field and properties of the Lie superalgebra

Provides new insights into the structure of enveloping algebras of Lie superalgebras

Abstract

Let L be a Lie superalgebra over a fled of characteristic p\neq 2 with enveloping algebra U(L) or let L be a restricted Lie superalgebra over a field of characteristic p > 2 with restricted enveloping algebra u(L). In this note, we establish when u(L) or U(L) is bounded Lie Engel.