RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.: Year: Volume: Issue: Page: Find

 Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2013, Volume 13, Issue 4(2), Pages 93–98 (Mi isu476)

Mathematics

About generating set of the invariant subalgebra of free restricted Lie algebra

V. M. Petrogradskya, I. A. Subbotinb

a Department of Mathematics, University of Brasilia, 70910-900 Brasilia DF, Brazil
b Ulyanovsk State University, Russia, 432970, Ulyanovsk, ul. L'va Tolstogo, 42

Abstract: Suppose that $L=L(X)$ is the free Lie p-algebra of finite rank $k$ with free generating set $X=\{x_1,…,x_k\}$ on a field of positive characteristic. Let $G$ is nontrivial finite group of homogeneous automorphisms $L(X)$. Our main purpose to prove that $L^G$ subalgebra of invariants is is infinitely generated. We have more strongly result. Let $Y=\cup_{n=1}^\infty Y_n$ be homogeneous free generating set for the algebra of invariants $L^G$, elements $Y_n$ are of degree $n$ relatively $X$, $n\ge1$. Consider the corresponding generating function $\mathscr H(Y,t)=\sum_{n=1}^\infty|Y_n|t^n$. In our case of free Lie restricted algebras, we prove, that series $\mathscr H(Y,t)$ has a radius of convergence $1/k$ and describe its growth at $t\to1/k-0$. As a result we obtain that the sequence $|Y_n|$, $n\ge1$, has exponential growth.

Key words: free Lie algebras, Lie p-algebras, invariants, generating set.

Full text: PDF file (163 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 501.1

Citation: V. M. Petrogradsky, I. A. Subbotin, “About generating set of the invariant subalgebra of free restricted Lie algebra”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:4(2) (2013), 93–98

Citation in format AMSBIB
\Bibitem{PetSub13} \by V.~M.~Petrogradsky, I.~A.~Subbotin \paper About generating set of the invariant subalgebra of free restricted Lie algebra \jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform. \yr 2013 \vol 13 \issue 4(2) \pages 93--98 \mathnet{http://mi.mathnet.ru/isu476}