FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1995, VOLUME 1, NUMBER 4, PAGES 989-1007
On types of overexponential growth in Lie PI-algebras
V.M.Petrogradsky
The growth function of identities $c_n (\mathcal{V})$
for varieties of Lie algebras is studied; where
$c_n (\mathcal{V})$ is the dimension
of a linear span of multilinear words in n
distinct letters in a free algebra $F(\mathcal{V},X)$
of the variety $\mathcal{V}$.
The main results are as follows: the description of types of overexponential growth is
suggested; the growth of identities for polynilpotent varieties is found. A complexity
function $\mathcal{C} (\mathcal{V},z)$ is
used; it corresponds to any nontrivial variety of Lie
algebras $\mathcal{V}$ and is an entire function
of a complex variable.
All articles are
published in Russian.
Location: http://mech.math.msu.su/~fpm/eng/95/954/95410.htm
Last modified: October 3, 1997.