IJPAM: Volume 95, No. 4 (2014)
PRIMITIVE SETS OF FREE LIE ALGEBRAS
Department of Mathematics
Abstract. Let and be free Lie algebras of finite rank and respectively and be a homomorphism from to . We prove that the preimage of a primitive set of contains a primitive set of . As a consequence of this result we obtain that an element of a subalgebra of is primitive in if it is primitive in .
Also we show that in a free Lie algebra of the form
if the ideal
of this algebra
contains a primitive element then and are conjugate by means of
an inner automorphism.
Received: April 11, 2014
AMS Subject Classification: 17B01, 17B40
Key Words and Phrases: primitive element, free Lie algebra
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DOI: 10.12732/ijpam.v95i4.5 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Pages: 535 -