Gr\"obner-Shirshov bases for free partially commutative Lie algebras
Yuqun Chen, Qiuhui Mo
TL;DR
This paper develops Gr"obner-Shirshov bases for free partially commutative Lie algebras using the Composition-Diamond lemma, providing a normal form and advancing algebraic computational methods.
Contribution
It introduces a Gr"obner-Shirshov basis for free partially commutative Lie algebras, extending algebraic tools to this class of Lie algebras.
Findings
Established a Gr"obner-Shirshov basis for the algebra
Derived a normal form for the algebra
Enhanced computational techniques in Lie algebra theory
Abstract
In this paper, by using Composition-Diamond lemma for Lie algebras, we give a Gr\"obner-Shirshov basis for free partially commutative Lie algebra over a commutative ring with unit. As an application, we obtain a normal form for such a Lie algebra.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Geometric and Algebraic Topology