Bases for partially commutative Lie algebras
Evgeny Poroshenko
TL;DR
This paper develops linear bases for partially commutative Lie algebras using Gröbner–Shirshov bases, demonstrating that the equality problem is algorithmically solvable for these structures.
Contribution
It introduces a method to find linear bases for partially commutative Lie algebras and shows the equality problem is solvable.
Findings
Linear bases for partially commutative Lie algebras are constructed.
The equality problem is algorithmically solvable for these algebras.
Abstract
In this paper, linear bases for the partially commutative Lie algebras are found. The method of the Gr\"{o}bner--Shirshov bases is used. It easily follows from the structure that the equality problem is algorithmically solvable for the partially commutative Lie algebras.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Topics in Algebra · Commutative Algebra and Its Applications