Alexander Pozhidaev
Sobolev Institute of Mathematics, Russia
Dialgebras and related systems.
Abstract: Dialgebras, i.e., algebraical systems with two associative operations that agree among themselves were introduced by J.-L. Loday as universal enveloping algebras for the Leibniz algebras. We discuss connection of dialgebras with different algebraical systems such as Leibniz-Poisson algebras, conformal algebras, Lie triple systems, and some others. Given a variety of algebras V, we also consider the concept of a dialgebra in V due to P.Kolesnikov.