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Abstract In this paper, we develop Gröbner–Shirshov basis theory for symmetric brace algebras. As applications, firstly, we give an alternative proof that the category of symmetric brace algebras is isomorphic… Click to show full abstract
Abstract In this paper, we develop Gröbner–Shirshov basis theory for symmetric brace algebras. As applications, firstly, we give an alternative proof that the category of symmetric brace algebras is isomorphic to the category of pre-Lie algebras, secondly, we prove that each pre-Lie algebra can be embedded into a simple pre-Lie algebra, and finally, we present a new linear basis for the universal pre-Lie algebra of a Lie algebra.
Keywords:
symmetric brace;
bner shirshov;
lie algebra;
pre lie;
brace algebras
Journal Title: Communications in Algebra
Year Published: 2020
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Journal Title: Communications in Algebra
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!