ABSTRACT
The theory of finite-dimensional associative algebras is one of the ancient areas of the modern algebra. The classification problem of associative algebras can be reduced to the classification problem of semisimple and nilpotent associative algebras. Since semisimple algebras are completely described by the well-known theory of Cartan-Killing the classification problem of Lie algebras reduces to the study of solvable algebras. The classification of nilpotent Lie algebras in higher dimensions remains a vast open area. The chapter summarizes basic facts about some classes of algebras which are closely related to Leibniz algebras. Therefore, a faithful representation of Leibniz algebras can be obtained easier than a faithful representation in the case of Lie algebras. The result intertwining diassociative algebras and dendriform algebras are best expressed in the framework of algebraic operads. The notion of diassociative algebra defines an algebraic operad Dias, which is binary and quadratic.
