FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2009, VOLUME 15, NUMBER 1, PAGES 117-124

**On invariants of modular free Lie algebras**

V. M. Petrogradsky

A. A. Smirnov

Abstract

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Suppose that $L(X)$ is a free Lie
algebra of finite rank over a field of positive characteristic.
Let $G$ be
a nontrivial finite group of homogeneous automorphisms of
$L(X)$.
It is known that the subalgebra of invariants $H\; =\; LG$ is
infinitely generated.
Our goal is to describe how big its free generating set is.
Let $Y\; =$È _{n=1}^{¥}Y_{n} be
a homogeneous free generating set of $H$, where elements
of $Y$_{n} are of
degree $n$
with respect to $X$.
We describe the growth of the generating function of $Y$ and prove that
$|Y$_{n}|
grow exponentially.

Location: http://mech.math.msu.su/~fpm/eng/k09/k091/k09108h.htm

Last modified: December 2, 2009