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arXiv · 1709.01401

Groebner-Shirshov bases for brace algebras

Yu Li·Qiuhui Mo·Xiangui Zhao
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Abstract

Let $A$ be a brace algebra. This structure implies that $A$ is also a pre-Lie algebra. In this paper, we establish Composition-Diamond lemma for brace algebras. Using this Composition-Diamond lemma we prove that each pre-Lie algebra $L$ can be embedded into a brace algebra $A_L$, i.e., $L$ is a pre-Lie subalgebra of $A_L$ up to isomorphism. We also determine an explicit linear basis for the brace algebra $A_{L}$.

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Yu Li, Qiuhui Mo, Xiangui Zhao. 2017-09-03. Groebner-Shirshov bases for brace algebras. https://arxiv.org/abs/1709.01401

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