Quasi Qn-Filiform Lie Algebras

In this paper, we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and by applying some properties of the root space decomposition, we obtain their isomorphism theorem.

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Controllability of quantum mechanical systems by root space decomposition of su(N)

Journal of Mathematical Physics ◽

10.1063/1.1467611 ◽

2002 ◽

Vol 43 (5) ◽

pp. 2051 ◽

Cited By ~ 121

Author(s):

Claudio Altafini

Keyword(s):

Mechanical Systems ◽

Quantum Mechanical ◽

Root Space ◽

Space Decomposition ◽

Quantum Mechanical Systems

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Links among Characteristically Nilpotent, $C$-Graded and Derived Filiform Lie Algebras

Rocky Mountain Journal of Mathematics ◽

10.1216/rmjm/1181069676 ◽

2005 ◽

Vol 35 (4) ◽

pp. 1081-1098

Author(s):

J.C. Benjumea ◽

F.J. Echarte ◽

M.C. Márquez ◽

J. Núñez

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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Derivation algebra of semi-direct sum of Lie algebras

Asian-European Journal of Mathematics ◽

10.1142/s1793557122500632 ◽

2021 ◽

pp. 2250063

Author(s):

Mohammad Reza Alemi ◽

Farshid Saeedi

Keyword(s):

Lie Algebras ◽

Arbitrary Field ◽

Direct Sum ◽

Derivation Algebra

Let [Formula: see text] and [Formula: see text] be two Lie algebras over an arbitrary field [Formula: see text], and let [Formula: see text] be the semidirect sum of [Formula: see text] by [Formula: see text]. In this paper, we give the structure of derivation algebra of [Formula: see text]; then as a consequence we illustrate the structure and dimension derivation algebra of Heisenberg Lie algebras.

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Solvable infinite filiform Lie algebras

Journal of Commutative Algebra ◽

10.1216/jca-2010-2-4-429 ◽

2010 ◽

Vol 2 (4) ◽

pp. 429-436 ◽

Cited By ~ 2

Author(s):

Clas Löfwall

Keyword(s):

Lie Algebras ◽

Filiform Lie Algebras

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AUTOMORPHISMS OF CERTAIN NILPOTENT LIE ALGEBRAS OVER COMMUTATIVE RINGS

International Journal of Algebra and Computation ◽

10.1142/s021819670700372x ◽

2007 ◽

Vol 17 (03) ◽

pp. 527-555 ◽

Cited By ~ 5

Author(s):

YOU'AN CAO ◽

DEZHI JIANG ◽

JUNYING WANG

Keyword(s):

Automorphism Group ◽

Commutative Ring ◽

Lie Algebra ◽

Lie Algebras ◽

Commutative Rings ◽

Nilpotent Lie Algebras ◽

Simple Lie Algebra ◽

Finite Dimensional ◽

Positive Roots ◽

Nilpotent Subalgebra

Let L be a finite-dimensional complex simple Lie algebra, Lℤ be the ℤ-span of a Chevalley basis of L and LR = R⊗ℤLℤ be a Chevalley algebra of type L over a commutative ring R. Let [Formula: see text] be the nilpotent subalgebra of LR spanned by the root vectors associated with positive roots. The aim of this paper is to determine the automorphism group of [Formula: see text].

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On Automorphisms and Derivations of a Lie Algebra

Algebra Colloquium ◽

10.1142/s1005386706000149 ◽

2006 ◽

Vol 13 (01) ◽

pp. 119-132 ◽

Cited By ~ 1

Author(s):

V. R. Varea ◽

J. J. Varea

Keyword(s):

Automorphism Group ◽

Normal Subgroup ◽

Large Class ◽

Lie Algebra ◽

Lie Algebras ◽

Finite Dimension ◽

Nilpotent Lie Algebra ◽

Identity Component ◽

Trivial Center

We study automorphisms and derivations of a Lie algebra L of finite dimension satisfying certain centrality conditions. As a consequence, we obtain that every nilpotent normal subgroup of the automorphism group of L is unipotent for a very large class of Lie algebras. This result extends one of Leger and Luks. We show that the automorphism group of a nilpotent Lie algebra can have trivial center and have yet a unipotent identity component.

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Derivations and Automorphism Group of Completed Witt Lie Algebra

Algebra Colloquium ◽

10.1142/s1005386712000454 ◽

2012 ◽

Vol 19 (03) ◽

pp. 581-590 ◽

Cited By ~ 1

Author(s):

Yongping Wu ◽

Ying Xu ◽

Lamei Yuan

Keyword(s):

Finite Element ◽

Automorphism Group ◽

Lie Algebra ◽

Cohomology Group ◽

Locally Finite ◽

Simple Lie Algebra ◽

Derivation Algebra ◽

First Cohomology Group

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a by-product, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad -locally finite element.

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