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ON THE FIXED POINTS OF AFINITE GROUP ACTING ON A RELATIVELY FREE LIE ALGEBRA

Published online by Cambridge University Press:  01 May 2000

R. M. BRYANT  and
A. I. PAPISTAS
R. M. BRYANT
Affiliation:
Department of Mathematics, UMIST, Manchester, M60 1QD, United Kingdom. E-mail: [email protected]
A. I. PAPISTAS
Affiliation:
Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, GR 54006, Greece. E-mail: [email protected]
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Abstract

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We show that if F is a free Lie algebra of rank at least 2 and if G is a non-trivial finite group of automorphisms of F then the fixed point subalgebra F^G is not finitely generated. Some similar results are proved for relatively free Lie algebras.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 2 , May 2000 , pp. 167 - 181
Copyright
2000 Glasgow Mathematical Journal Trust