Identities of Algebras and their Representations

Preliminary results Characters and $\alpha$-functions on 2 -words and varieties of representations of Lie algebras distinguished by them $\alpha$-functions related to the killing form and to irreducible representations of semisimple Lie algebras. Central polynomials of irreducible representations of reductive Lie algebras $\alpha$-functions related to full matrix algebras. Trace identities and central polynomials of full matrix algebras $M_n$ and matrix superalgebras $M_{n,k}$ The $alpha$-function related to representations of the simple three-dimensional Lie algebra $\mathfrak g$ and its applications to varieties of groups and associative algebras Varieties generated by Lie algebras of Cartan type Algebraic supplements.