Malcev-like anti-commutative algebras

Abstract: The tangent algebras of local analytic Moufang and diassociative loops are Malcev algebras and binary Lie algebras introduced by A. I. Malcev. Their classifications in low dimension are given by the works on E. N. Kuzmin and A. T. Gainov. In the talk we discuss the classification of solvable anti-commutative algebras that have the same decomposition properties as solvable Malcev or binary Lie algebras. The classification result enables us to find and study a family of binary Lie algebras for which the closed form of the Baker-Campbell- Hausdorff series defines the multiplication function of an analytic diassociative loop on the entire binary Lie algebra.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar