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Deformationen und Degenerationen von Liealgebren und LiegruppenDaboul, Claudia. January 1999 (has links)
Hamburg, Universiẗat, Diss., 1999. / Dateiformat: zip, Dateien im PDF-Format.
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"Alfa"-conexões obtidas por ações de grupos LieFernandes, Marco Antonio Nogueira 21 August 1992 (has links)
Orientador: Luiz Antonio Barrera San Martin / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Científica / Made available in DSpace on 2018-07-17T08:56:10Z (GMT). No. of bitstreams: 1
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Previous issue date: 1992 / Resumo: Não informado. / Abstract: Not informed. / Doutorado / Doutor em Matemática
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Cohomologie et déformation des champs de vecteurs sur une variété de dimension 1 / Cohomology and deformation of vector fields on a variety of dimensions 1Bartouli, Issam 20 June 2019 (has links)
On considère la structure du Vect(R)-module sur les espaces des opérateurs différentiels bilinéaires agissant sur les espaces de densités. On calcule la première cohomologie différentielle des champs de vecteurs d’algèbre de Lie Vect(R) avec des coefficients dans l’espace des opérateurs différentiels bilinéaires agissant sur les densités pondérées.On considère l’action de Vect(S1) par la dérivée de Lie sur les espaces d’opérateurs pseudodifférentiels DO. On étudie les déformations h-triviales de l’intégration standard de l’algèbre de Lie Vect(S1) de champs de vecteurs lisses sur le cercle, dans l’algèbre de Lie de fonctions sur le fibré cotangent T*S1. On classe les déformations de cette action qui deviennent triviales une fois limitées à h où h = aff(1) ou sl(2). Les conditions nécessaires et suffisantes pour l’intégrabilité des déformations infinitésimales sont données. / We consider the Vect(R)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities.We compute the first differential cohomology of the vector fields Lie algebra Vect(R) with coefficients in space of bilinear differential operators acting on weighted densities. we consider the action of Vect(S1) by Lie derivative on the spaces of pseudodifferential operators . We study the h-trivial deformations of the standard embedding of the Lie algebra Vect(S1) of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle T∗S1. We classify the deformations of this action that become trivial once restricted to h, where h = aff(1) or sl(2). Necessary and sufficient conditions for integrability of infinitesimal deformations are given.
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Simetrias de Lie de equações a derivadas fracionárias e íntegro-diferenciaisSilva Júnior, Carlos César da 28 July 2016 (has links)
Dissertação (mestrado)—Universidade de Brasília, Instituto de Física, Programa de Pós-Graduação em Física, 2016. / Submitted by Fernanda Percia França (fernandafranca@bce.unb.br) on 2016-08-19T17:32:34Z
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2016_CarlosCésardaSilvaJúnior.pdf: 406403 bytes, checksum: dd360fb49ecc7658d0ec18c72c90019b (MD5) / Nesta dissertação, são discutidos alguns modelos para encontrar geradores de simetrias de Lie. Essas simetrias são importantes para mapear soluções (embora a princípio esse ponto não seja o foco desse trabalho). Os modelos classícos da simetria de Lie são apresentados, e com eles, modelos para encontrar simetrias de equações íntegro-diferenciais e fracionarias são construídos. Geradores de uma mesma equação são encontrados usando dois modelos diferentes, com o objetivo de demonstrar a equivalência entre esses modelos.
_________________________________________________________________________________________________ ABSTRACT / This dissertation will discuss about some methods to find Lie’ssymmetry generators. These symmetries are important to map solutions (although it will not be considered the focus of this work). Classic Lie’ssymmetry methods are presented, and alongside with them, other methods of Integro-differential and fractional equations are built to find symmetries. Generators from the same equation are found by using two different models, aiming to demonstrate equivalence between these methods.
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Lie symmetry analysis of certain nonlinear evolution equations of mathematical physics / Abdullahi Rashid Adem.Adem, Abdullahi Rashid January 2013 (has links)
In this work we study the applications of Lie symmetry analysis to certain nonlinear
evolution equations of mathematical physics. Exact solutions and conservation laws
are obtained for such equations. The equations which are considered in this thesis
are a generalized Korteweg-de Vries-Burgers equation, a two-dimensional integrable
generalization of the Kaup-Kupershmidt equation, a coupled Korteweg-de Vries system,
a generalized coupled variable-coefficient modified Korteweg-de Vries system, a
new coupled Korteweg-de Vries system and a new coupled Kadomtsev-Petviashvili
system.
The generalized Korteweg-de Vries-Burgers equation is investigated from the point
of view of Lie group classification. We show that this equation admits a four-dimensional
equivalence Lie algebra. It is also shown that the principal Lie algebra
consists of a single translation symmetry. Several possible extensions of the principal
Lie algebra are computed and their associated symmetry reductions and exact
solutions are obtained.
The Lie symmetry method is performed on a two-dimensional integrable generalization
of the Kaup-Kupershmidt equation. Exact solutions are obtained using the
Lie symmetry method in conjunction with the extended tanh method and the extended
Jacobi elliptic function method. In addition to exact solutions we also present
conservation laws which are derived using the multiplier approach.
A coupled Korteweg-de Vries system and a generalized coupled variable-coefficient
modified Korteweg-de Vries system are investigated using Lie symmetry analysis.
The similarity reductions and exact solutions with the aid of simplest equations
and Jacobi elliptic function methods are obtained for the coupled Korteweg-de Vries
system and the generalized coupled variable-coefficient modified Korteweg-de Vries
system. In addition to this, the conservation laws for the two systems are derived
using the multiplier approach and the conservation theorem due to Ibragimov.
Finally, a new coupled Korteweg-de Vries system and a new coupled Kadomtsev
Petviashvili system are analyzed using Lie symmetry method. Exact solutions are
obtained using the Lie symmetry method in conjunction with the simplest equation,
Jacobi elliptic function and (G'/G)-expansion methods. Conservation laws are also
obtained for both the systems by employing the multiplier approach. / Thesis (PhD.(Applied Mathematics) North-West University, Mafikeng Campus, 2013
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Algebra de Lie de un grupo de trenza puraQuesada Llanto, Julio Christian January 2014 (has links)
En este trabajo estudiamos el álgebra de Lie asociado con la filtración de la serie central del grupo de trenzas pura de Artin y probamos que es una extensión de
las álgebras de Lie libres.
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Tangent and cotangent bundles automorphism groups and representations of Lie groups /Hindeleh, Firas. January 2006 (has links)
Thesis (Ph.D.)--University of Toledo, 2006. / Typescript. "A dissertation [submitted] as partial fulfillment of the requirements of the Doctor of Philosophy degree in Mathematics." Bibliography: leaves 79-82.
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Some aspects of formal lie groupsGeorgoudis, John. January 1968 (has links)
No description available.
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An infinitesimal approach to Lie groups and applicationsGould, Mark David January 1979 (has links)
1 v. (various paging) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.1980) from the Dept. of Mathematical Physics, University of Adelaide
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An infinitesimal approach to Lie groups and applications.Gould, Mark David. January 1979 (has links) (PDF)
Thesis (Ph.D. 1980) from the Department of Mathematical Physics, University of Adelaide.
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