Asymptotic Behavior in Lie Nilpotent Relatively Free Algebras and Extended Grassmann Algebras.

The present paper is devoted to estimating the codimensions cn for the variety of associative algebras given by the identity [x1, ..., xl] = 0 for odd l. The characteristic of the ground field is different from 2 and 3. The construction of the so-called extended Grassmann algebra is applied very effectively. [ABSTRACT FROM AUTHOR]