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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. For each pre-Lie… Click to show full abstract
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. For each pre-Lie algebra L, we find a Gröbner–Shirshov basis for its universal brace algebra Ub(L). As applications, we determine an explicit linear basis for Ub(L) and prove that L is a pre-Lie subalgebra of Ub(L).
Keywords:
shirshov bases;
bases brace;
bner shirshov;
pre lie;
brace algebras
Journal Title: Communications in Algebra
Year Published: 2017
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Journal Title: Communications in Algebra
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!