Lie triple derivations of the nilpotent subalgebra of Dm

2017 ◽  
Vol 11 ◽  
pp. 283-285
Author(s):  
Hailing Li ◽  
Ying Wang
Keyword(s):  
Nilpotent Subalgebra

AUTOMORPHISMS OF CERTAIN NILPOTENT LIE ALGEBRAS OVER COMMUTATIVE RINGS

2007 ◽  
Vol 17 (03) ◽  
pp. 527-555 ◽  
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].

scholarly journals The maximum dimension of a Lie nilpotent subalgebra of $\boldsymbol {\mathbb {M}_n(F)}$ of index $\boldsymbol {m}$

2019 ◽  
Vol 372 (7) ◽  
pp. 4553-4583
Author(s):  
J. Szigeti ◽  
J. van den Berg ◽  
L. van Wyk ◽  
M. Ziembowski
Keyword(s):  
Maximum Dimension ◽  
Nilpotent Subalgebra

scholarly journals GEOMETRICAL DESCRIPTION OF THE LOCAL INTEGRALS OF MOTION OF MAXWELL-BLOCH EQUATION

1995 ◽  
Vol 10 (17) ◽  
pp. 1209-1223 ◽  
Author(s):  
A.V. ANTONOV ◽  
B.L. FEIGIN ◽  
A.A. BELOV
Keyword(s):  
Phase Space ◽  
Homogeneous Space ◽  
Lie Algebra ◽  
Bloch Equation ◽  
Integrals Of Motion ◽  
Positive Part ◽  
Abelian Subalgebra ◽  
Hamiltonian Flows ◽  
Nilpotent Subalgebra ◽  
Lattice Setting

We represent a classical Maxwell-Bloch equation and relate it to positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra [Formula: see text] on a Maxwell–Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show that Hamiltonian flows associated with the Maxwell–Bloch local integrals of motion (i.e. positive AKNS flows) are identified with an infinitesimal action of an Abelian subalgebra of the nilpotent subalgebra n− on a Maxwell–Bloch phase space. Possibilities of quantization and lattice setting of Maxwell–Bloch equation are discussed.

BURNSIDE AND KUROSH PROBLEMS

2004 ◽  
Vol 14 (02) ◽  
pp. 197-211 ◽  
Author(s):  
LAKHDAR HAMMOUDI
Keyword(s):  
Residually Finite ◽  
Nonassociative Algebras ◽  
Nilpotent Subalgebra

For any integer d≥2 and over any field [Formula: see text], we construct a residually finite nonnilpotent nil algebra over [Formula: see text] generated by d elements such that any d-1 elements generate a nilpotent subalgebra. This leads to analogous results for nonassociative algebras and groups. In our proof we do not use the well-known Golod-Šafareviš lemma.

scholarly journals Nilpotent Lie algebras of derivations with the center of small corank

2020 ◽  
Vol 12 (1) ◽  
pp. 189-198
Author(s):  
Y.Y. Chapovskyi ◽  
L.Z. Mashchenko ◽  
A.P. Petravchuk
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Characteristic Zero ◽  
Integral Domain ◽  
Natural Basis ◽  
Nilpotent Lie Algebras ◽  
Locally Nilpotent ◽  
Nilpotent Subalgebra

Let $\mathbb K$ be a field of characteristic zero, $A$ be an integral domain over $\mathbb K$ with the field of fractions $R=Frac(A),$ and $Der_{\mathbb K}A$ be the Lie algebra of all $\mathbb K$-derivations on $A$. Let $W(A):=RDer_{\mathbb K} A$ and $L$ be a nilpotent subalgebra of rank $n$ over $R$ of the Lie algebra $W(A).$ We prove that if the center $Z=Z(L)$ is of rank $\geq n-2$ over $R$ and $F=F(L)$ is the field of constants for $L$ in $R,$ then the Lie algebra $FL$ is contained in a locally nilpotent subalgebra of $ W(A)$ of rank $n$ over $R$ with a natural basis over the field $R.$ It is also proved that the Lie algebra $FL$ can be isomorphically embedded (as an abstract Lie algebra) into the triangular Lie algebra $u_n(F)$, which was studied early by other authors.

scholarly journals On the solvability of graded Novikov algebras

2021 ◽  
pp. 1-14
Author(s):  
Ualbai Umirbaev ◽  
Viktor Zhelyabin
Keyword(s):  
Solvable Group ◽  
Finite Solvable Group ◽  
Group Of Automorphisms ◽  
Novikov Algebra ◽  
Novikov Algebras ◽  
Nilpotent Subalgebra ◽  
The Right ◽  
Text Component

We show that the right ideal of a Novikov algebra generated by the square of a right nilpotent subalgebra is nilpotent. We also prove that a [Formula: see text]-graded Novikov algebra [Formula: see text] over a field [Formula: see text] with solvable [Formula: see text]-component [Formula: see text] is solvable, where [Formula: see text] is a finite additive abelean group and the characteristic of [Formula: see text] does not divide the order of the group [Formula: see text]. We also show that any Novikov algebra [Formula: see text] with a finite solvable group of automorphisms [Formula: see text] is solvable if the algebra of invariants [Formula: see text] is solvable.

Lie Algebras with Nilpotent Centralizers

1979 ◽  
Vol 31 (5) ◽  
pp. 929-941 ◽  
Author(s):  
G. M. Benkart ◽  
I. M. Isaacs
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Simple Lie Algebras ◽  
Arbitrary Characteristic ◽  
Algebra For All ◽  
Finite Dimensional ◽  
Nilpotent Subalgebra ◽  
Finite Dimensional Lie Algebras

We consider finite dimensional Lie algebras over an algebraically closed field F of arbitrary characteristic. Such an algebra L will be called a centralizer nilpotent Lie algebra (abbreviated c.n.) provided that the centralizer C(x) is a nilpotent subalgebra of L for all nonzero x ∈ L.For each algebraically closed F, there is a unique simple Lie algebra of dimension 3 over F which we shall denote S(F). This algebra has a basis e−1, e0, e1 such that [e−1e0] = e−1, [e−1e1] = e0 and [e0e1] = e1. (If char(F) ≠ 2, then S(F) ≅ sl2(F).) It is trivial to check that S(F) is a c.n. algebra for all F.There are two other types of simple Lie algebras we consider. If char (F) = 3, construct the octonion (Cayley) algebra over F.

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