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.

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Last modified: December 2, 2009