Results 61 to 70 of about 3,483,162 (228)
On the isomorphism problem for $C^*$-algebras of nilpotent Lie groups [PDF]
, 2018 We investigate to what extent a nilpotent Lie group is determined by its $C^*$-algebra. We prove that, within the class of exponential Lie groups, direct products of Heisenberg groups with abelian Lie groups are uniquely determined even by their unitary dual, while nilpotent Lie groups of dimension $\le 5$ are uniquely determined by the Morita ...
arxiv +1 more source
MOVING FRAMES AND NOETHER’S CONSERVATION LAWS—THE GENERAL CASE
Forum of Mathematics, Sigma, 2016 In recent works [Gonçalves and Mansfield, Stud. Appl. Math., 128 (2012), 1–29; Mansfield, A Practical Guide to the Invariant Calculus (Cambridge University Press, Cambridge, 2010)], the authors considered various Lagrangians, which are invariant under a ...
TÂNIA M. N. GONÇALVES +1 more
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Advances in Difference Equations, 2021 In this study, we investigate a new fourth-order integrable nonlinear equation. Firstly, by means of the efficient Hirota bilinear approach, we establish novel types of solutions which include breather, rogue, and three-wave solutions. Secondly, with the
Dumitru Baleanu +2 more
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Nonlinear potential filtration equation and global actions of Lie symmetries
Electronic Journal of Differential Equations, 2009 The Lie point symmetries of the nonlinear potential filtration equation break into five cases. Contact symmetries provide another two cases. By restricting to a natural class of functions, we show that these symmetries exponentiate to a global action ...
Mark R. Sepanski
doaj
2-step nilpotent Lie groups arising from semisimple modules [PDF]
arXiv, 2008 Every finite dimensional real representation of a compact real semisimple Lie algebra determines a metric 2-step nilpotent Lie algebra and a corresponding simply connected metric 2-step nilpotent Lie group N. We study the differential geometry of N using representation theory of the complexified complex semisimple Lie algebra.
arxiv
Bases for representation rings of Lie groups and their maximal tori [PDF]
arXiv, 2015 A Lie group is a group that is also a differentiable manifold, such that the group operation is continuous respect to the topological structure. To every Lie group we can associate its tangent space in the identity point as a vector space, which is its Lie algebra.
arxiv
Group algebras of finite groups as Lie algebras [PDF]
arXiv, 2008 We consider the natural Lie algebra structure on the (associative) group algebra of a finite group $G$, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of $G$.
arxiv
An Elementary Introduction to Groups and Representations [PDF]
Expanded version published by Springer-Verlag, Graduate Texts in
Mathematics #222, 2003, 2000 These notes give an elementary introduction to Lie groups, Lie algebras, and their representations. Designed to be accessible to graduate students in mathematics or physics, they have a minimum of prerequisites. Topics include definitions and examples of Lie groups and Lie algebras, the relationship between Lie groups and Lie algebras via the ...
arxiv
Volume of representation varieties
, 2002 We introduce the notion of volume of the representation variety of a finitely presented discrete group in a compact Lie group using the push-forward measure associated to a map defined by a presentation of the discrete group. We show that the volume thus
Mulase, Motohico, Penkava, Michael
core +1 more source
On the Moore Formula of Compact Nilmanifolds
Symmetry, Integrability and Geometry: Methods and Applications, 2009 Let G be a connected and simply connected two-step nilpotent Lie group and Γ a lattice subgroup of G. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations involved in the decomposition ...
Hatem Hamrouni
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