FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 3, PAGES 135-148

On $T$-spaces and relations in relatively free, Lie nilpotent, associative algebras

A. V. Grishin
L. M. Tsybulya
A. A. Shokola

Abstract

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The purpose of this work is to obtain the commutator relations and Frobenius relations in a relatively free algebra $F(l)$ specified by the identity $[x$₁,...,x_l]=0 over a field of characteristic $p\; >\; 0$. These relations for $l\; >\; 3$ are analogous to the relations in the algebra $F(3)$ and are applied to the $T$-spaces in the algebra $F(l)$. In order to study the relations in $F(l)$ in more detail, we construct a model algebra analogous to the Grassmann algebra.

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Last modified: March 24, 2011