scholarly journals A Characterisation of Nilpotent Lie Algebras by Invertible Leibniz-Derivations

2013 ◽  
Vol 41 (7) ◽  
pp. 2427-2440 ◽  
Author(s):  
Wolfgang Alexander Moens
Keyword(s):  
Lie Algebras ◽  
Nilpotent Lie Algebras

Central automorphisms of free nilpotent Lie algebras

2017 ◽  
Vol 16 (11) ◽  
pp. 1750205
Author(s):  
Özge Öztekin ◽  
Naime Ekici
Keyword(s):  
Lie Algebras ◽  
Finite Rank ◽  
Characteristic Zero ◽  
Sufficient Conditions ◽  
Nilpotency Class ◽  
Nilpotent Lie Algebra ◽  
Central Automorphism ◽  
Nilpotent Lie Algebras ◽  
Central Automorphisms

Let [Formula: see text] be the free nilpotent Lie algebra of finite rank [Formula: see text] [Formula: see text] and nilpotency class [Formula: see text] over a field of characteristic zero. We give a characterization of central automorphisms of [Formula: see text] and we find sufficient conditions for an automorphism of [Formula: see text] to be a central automorphism.

scholarly journals KONTSEVICH'S UNIVERSAL FORMULA FOR DEFORMATION QUANTIZATION AND THE CAMPBELL–BAKER–HAUSDORFF FORMULA

2000 ◽  
Vol 11 (04) ◽  
pp. 523-551 ◽  
Author(s):  
VINAY KATHOTIA
Keyword(s):  
Lie Algebras ◽  
Deformation Quantization ◽  
Differential Operators ◽  
Main Tool ◽  
Graphical Analysis ◽  
Poisson Structures ◽  
Nilpotent Lie Algebras ◽  
Enveloping Algebra ◽  
Universal Formula ◽  
The Given

We relate a universal formula for the deformation quantization of Poisson structures (⋆-products) on ℝd proposed by Maxim Kontsevich to the Campbell–Baker–Hausdorff (CBH) formula. We show that Kontsevich's formula can be viewed as exp (P) where P is a bi-differential operator that is a deformation of the given Poisson structure. For linear Poisson structures (duals of Lie algebras) his product takes the form exp (C+L) where exp (C) is the ⋆-product given by the universal enveloping algebra via symmetrization, essentially the CBH formula. This is established by showing that the two products are identical on duals of nilpotent Lie algebras where the operator L vanishes. This completely determines part of Kontsevich's formula and leads to a new scheme for computing the CBH formula. The main tool is a graphical analysis for bi-differential operators and the computation of certain iterated integrals that yield the Bernoulli numbers.

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].

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