On the laws of finite dimensional representations of solvable lie algebras and groups

1988 ◽  
pp. 114-129 ◽  
Author(s):  
A. N. Krasil'nikov ◽  
A. L. Šmel'kin
Keyword(s):  
Lie Algebras ◽  
Finite Dimensional ◽  
Solvable Lie Algebras

Subinvariance in Solvable Lie Algebras

1976 ◽  
Vol 28 (1) ◽  
pp. 181-185 ◽  
Author(s):  
Chong-Yun Chao ◽  
Ernest L. Stitzinger
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Solvable Case ◽  
Finite Dimensional ◽  
Solvable Lie Algebras ◽  
Carry Over ◽  
Subnormal Subgroups

In a recent paper, Wielandt has continued his investigation of subnormal subgroups. Since the analogous concept is also of interest in Lie algebras, this note considers the Lie algebra counterparts to Wielandt's results. Generally the results do not carry over to all Lie algebras, but do hold in the solvable case. In order to state the main results, several definitions are needed and consequently we begin by listing some of the consequences. All Lie algebras considered here are finite dimensional over a field.

The rigidity of some solvable Lie algebras

2018 ◽  
Vol 2018 (2) ◽  
pp. 43-49
Author(s):  
R.K. Gaybullaev ◽  
Kh.A. Khalkulova ◽  
J.Q. Adashev
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras

Integrable two-dimensional dynamical systems and the characteristic Lie algebras

2007 ◽  
Vol 5 ◽  
pp. 195-200
Author(s):  
A.V. Zhiber ◽  
O.S. Kostrigina
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Second Order ◽  
System Of Equations ◽  
Two Dimensional ◽  
Finite Dimensional ◽  
Dimensional Dynamical System

In the paper it is shown that the two-dimensional dynamical system of equations is Darboux integrable if and only if its characteristic Lie algebra is finite-dimensional. The class of systems having a full set of fist and second order integrals is described.

scholarly journals Hodge decomposition of string topology

2021 ◽  
Vol 9 ◽  
Author(s):  
Yuri Berest ◽  
Ajay C. Ramadoss ◽  
Yining Zhang
Keyword(s):  
Lie Algebras ◽  
General Theorem ◽  
Hodge Decomposition ◽  
String Topology ◽  
Free Loop Space ◽  
Oriented Manifold ◽  
Universal Enveloping Algebras ◽  
Finite Dimensional ◽  
Equivariant Homology ◽  
Simply Connected

Abstract Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$ -equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free loop space of X preserves the Hodge decomposition of $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture of [7].

Representations of filtered solvable Lie algebras

2012 ◽  
Vol 203 (1) ◽  
pp. 75-87
Author(s):  
Alexander N Panov
Keyword(s):  
Lie Algebras ◽  
Solvable Lie Algebras

Levi and Malcev Theorems for Finite-Dimensional Algebras from the Variety Defined by the Identities x2 = J( x,y, zu) =0

2021 ◽  
Vol 28 (01) ◽  
pp. 87-90
Author(s):  
Óscar Guajardo Garza ◽  
Marina Rasskazova ◽  
Liudmila Sabinina
Keyword(s):  
Lie Algebras ◽  
Present Article ◽  
Variety Of Algebras ◽  
Finite Dimensional ◽  
Finite Dimensional Algebras

We study the variety of binary Lie algebras defined by the identities [Formula: see text], where [Formula: see text] denotes the Jacobian of [Formula: see text], [Formula: see text], [Formula: see text]. Building on previous work by Carrillo, Rasskazova, Sabinina and Grishkov, in the present article it is shown that the Levi and Malcev theorems hold for this variety of algebras.

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