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

Fındık, Şehmus — 2012

Serdica Mathematical Journal

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 the formal power...

Outer endomorphisms of free metabelian Lie algebras

Findik, Sehmus — 2011

Serdica Mathematical Journal

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.

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