Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures

1990 ◽  
Vol 112 (4) ◽  
pp. 657 ◽  
Author(s):  
Marc A. Rieffel
Keyword(s):  
Lie Group ◽  
Poisson Structures ◽  
Convolution Algebras

scholarly journals Poisson structures on the cotangent bundle of a Lie group or a principle bundle and their reductions

1994 ◽  
Vol 35 (9) ◽  
pp. 4909-4927 ◽  
Author(s):  
D. Alekseevsky ◽  
J. Grabowski ◽  
G. Marmo ◽  
P. W. Michor
Keyword(s):  
Lie Group ◽  
Cotangent Bundle ◽  
Poisson Structures

HOLOMORPHIC SYMPLECTIC AND POISSON STRUCTURES ON THE HOLOMORPHIC COTANGENT BUNDLE OF A COMPLEX LIE GROUP AND OF A HOLOMORPHIC PRINCIPAL BUNDLE

2013 ◽  
Vol 06 (03) ◽  
pp. 1350029 ◽  
Author(s):  
Cristian Ida
Keyword(s):  
Lie Group ◽  
Cotangent Bundle ◽  
Principal Bundle ◽  
Poisson Structures

In this paper we introduce holomorphic symplectic and Poisson structures on the holomorphic cotangent bundle of a complex Lie group and of a holomorphic principal bundle.

scholarly journals DEFORMATION QUANTIZATION OF POISSON MANIFOLDS IN THE DERIVATIVE EXPANSION

2009 ◽  
Vol 06 (02) ◽  
pp. 219-224 ◽  
Author(s):  
A. V. BRATCHIKOV
Keyword(s):  
Poisson Bracket ◽  
Lie Group ◽  
Deformation Quantization ◽  
Second Order ◽  
Poisson Manifolds ◽  
Poisson Structures ◽  
Derivative Expansion ◽  
Order Deformation ◽  
Bracket Algebra ◽  
Derivatives Of

Deformation quantization of Poisson manifolds is studied within the framework of an expansion in powers of derivatives of Poisson structures. We construct the Lie group associated with a Poisson bracket algebra which defines a second order deformation in the derivative expansion.

Symmetry properties of fractional order transport equations

2012 ◽  
Vol 9 (1) ◽  
pp. 59-64
Author(s):  
R.K. Gazizov ◽  
A.A. Kasatkin ◽  
S.Yu. Lukashchuk
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Lie Group ◽  
Initial Conditions ◽  
Group Analysis ◽  
Equivalence Transformation ◽  
Point Change ◽  
Infinitesimal Operator ◽  
Symmetry Properties ◽  
Fractional Differential

In the paper some features of applying Lie group analysis methods to fractional differential equations are considered. The problem related to point change of variables in the fractional differentiation operator is discussed and some general form of transformation that conserves the form of Riemann-Liouville fractional operator is obtained. The prolongation formula for extending an infinitesimal operator of a group to fractional derivative with respect to arbitrary function is presented. Provided simple example illustrates the necessity of considering both local and non-local symmetries for fractional differential equations in particular cases including the initial conditions. The equivalence transformation forms for some fractional differential equations are discussed and results of group classification of the wave-diffusion equation are presented. Some examples of constructing particular exact solutions of fractional transport equation are given, based on the Lie group methods and the method of invariant subspaces.

ε‎-Invariance

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Algebra ◽  
Lie Group

The discussions up to Chapter 4 have been concerned with the Lie group. In this chapter, the Lie algebra is constructed by defining the operators ∇ and ∇̃.

The Centralizer

2018 ◽  
Author(s):  
Ercüment H. Ortaçgil
Keyword(s):  
Lie Group ◽  
Group Structure ◽  
Diffeomorphism Group ◽  
Group Diff ◽  
Local Solutions

The pseudogroup of local solutions in Chapter 3 defines another pseudogroup by taking its centralizer inside the diffeomorphism group Diff(M) of a manifold M. These two pseudogroups define a Lie group structure on M.

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

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