Displaying similar documents to “Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras”

Outer Automorphisms of Lie Algebras related with Generic 2×2 Matrices

Fındık, Şehmus (2012)

Serdica Mathematical Journal

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2010 Mathematics Subject Classification: 17B01, 17B30, 17B40, 16R30. Let Fm = Fm(var(sl2(K))) be the relatively free algebra of rank m in the variety of Lie algebras generated by the algebra sl2(K) over a field K of characteristic 0. Our results are more precise for m = 2 when F2 is isomorphic to the Lie algebra L generated by two generic traceless 2 × 2 matrices. We give a complete description of the group of outer automorphisms of the completion L^ of L with respect to...

Outer endomorphisms of free metabelian Lie algebras

Findik, Sehmus (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 17B01, 17B30, 17B40. Let Fm be the free metabelian Lie algebra of rank m over a field K of characteristic 0. We consider the semigroup IE(Fm) of the endomorphisms of Fm which are identical modulo the commutator ideal of Fm. We describe the factor semigroup of IE(Fm) modulo the congruence induced by the group of inner automorphisms.

The Automorphism Group of the Free Algebra of Rank Two

Cohn, P. (2002)

Serdica Mathematical Journal

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The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate...

An overview of free nilpotent Lie algebras

Pilar Benito, Daniel de-la-Concepción (2014)

Commentationes Mathematicae Universitatis Carolinae

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Any nilpotent Lie algebra is a quotient of a free nilpotent Lie algebra of the same nilindex and type. In this paper we review some nice features of the class of free nilpotent Lie algebras. We will focus on the survey of Lie algebras of derivations and groups of automorphisms of this class of algebras. Three research projects on nilpotent Lie algebras will be mentioned.

A Note on Automorphisms of Free Nilpotent Groups

Sandro Mattarei (2007)

Bollettino dell'Unione Matematica Italiana

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-- We exhibit normal subgroups of a free nilpotent group F of rank two and class three, which have isomorphic finite quotients but are not conjugate under any automorphism of F.