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We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner–Shirshov bases method for… Click to show full abstract
We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner–Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras (Lie di-algebras). As another application, we prove an analogue of the Poincare–Birkhoff–Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD!-algebra).
Keywords:
algebra;
shirshov bases;
bases replicated;
replicated algebras;
bner shirshov;
shirshov
Journal Title: Algebra Colloquium
Year Published: 2017
Link to full text (if available)
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Journal Title: Algebra Colloquium
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!