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What is Lie-admissible Algebras Study about?

In this paper, we study nonassociative algebras which satisfy the following identities: (xy)z = (yx)z,x(yz) = x(zy). These algebras are Lie-admissible algebras i.e., they become Lie algebras under the commutator [f, g] = fg − gf. We obtain a nonassociative Gr¨obner-Shirshov basis for the free algebra LA(X) with a generating set X of the above variety. As an application, we get a monomial basis for LA(X). We also give a characterization of the elements of S(X) among the elements of LA(X), where S(X) is the

Author

Ioan Degau

Language

EN