About enveloping algebras of direct sums
G\'erard Henry Edmond Duchamp (LIPN), Christophe Tollu (LIPN),, Jean-Gabriel Luque (GR2IF), Vu Nguyen Dinh (USTH)
TL;DR
This paper addresses the problem of normal ordering in the enveloping algebras of direct sums, providing solutions that extend the classical PBW theorem to this context.
Contribution
It introduces a method to solve the PBW-like problem for enveloping algebras of direct sums, advancing the understanding of their algebraic structure.
Findings
Established a PBW-like normal ordering for enveloping algebras of direct sums.
Extended classical PBW theorem to a broader class of algebraic structures.
Provided explicit solutions to the normal ordering problem.
Abstract
We solve the PBW-like problem of normal ordering for enveloping algebras of direct sums.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Advanced Algebra and Logic