New Developments in Lie Theory and Its Applications

Birkhäuser Boston eBooks, 1992

New Developments in Lie theory and their applications I edited by Juan Tirao, Nolan Wallach. p. cm.-(Progress in mathematics: 105) Papers from the Third Workshop on Representation Theory of Lie Groups and Their Applications, held Aug.-Sept. 1989 in C6rdoba, Argentina. Includes bibliographical references.

Banach Center Publications

After a quick presentation of the theory of Lie systems from a geometric perspective, recent progresses on their applications when compatible geometric structures exist will be described with a special emphasis in the particular case of admissible Kähler structures, and therefore with applications in Quantum Mechanics.

Journal of Generalized Lie Theory and Applications, 2012

Hom-algebra structures are given on linear spaces by multiplications twisted by linear maps. Hom-Lie algebras and general quasi-Hom-Lie and quasi-Lie algebras were introduced by Hartwig, Larsson and Silvestrov as algebras embracing Lie algebras, super and color Lie algebras and their quasi-deformations by twisted derivations. In this paper we introduce and study Hom-associative, Hom-Leibniz and Hom-Lie admissible algebraic structures generalizing associative, Leibniz and Lie admissible algebras. Also, we characterize flexible Hom-algebras and explain some connections and differences between Hom-Lie algebras and Santilli's isotopies of associative and Lie algebras.

Abstract and Applied Analysis, 2013

This special issue was planned to focus on most the recent advances in the applications of Lie groups. It covered a wide area of topics in interdisciplinary studies in mathematics, mechanics, physics, and finance. We were particularly interested in receiving novel contributions devoted to Lie groups, in particular, applications to specific problems in applied sciences. We aimed to bring together contributions across a variety of applications of Lie groups and invite researchers to submit original research and/or domain reviews in various topics. Potential topics included, but were not limited to the following: Lie algebras and Lie pseudogroups, optimal control, topological groups, representation theory of Lie algebras, differential geometry, finance, dynamical systems, quantum mechanics, super-symmetry and superintegrability, information theory, Lie theory and symmetry methods in differential, fractal differential, integrodifferential, and difference equations, and further applications in physics and mechanics.

A σ-ideal I on a Polish group (X, +) has Smital Property if for every dense set D and a Borel I-positive set B the algebraic sum D + B is a complement of a set from I. We consider several variants of this property and study their connections with countable chain condition, maximality and how well they are preserved via Fubini products.

Springer Proceedings in Mathematics & Statistics, 2013

Using our previous results on the systematic construction of invariant differential operators for non-compact semisimple Lie groups we classify the special reduced multiplets and minimal representations in the case of SO(p,q).

2008

Geometry and analysis of shape space. The core of shape space in one of its simplest forms is the orbit space of the action of the group of diffeomorphisms of the circle S1 (the reparametrization group) on the space of immersions of the circle into the plane R2. The aim is to find good Riemannian metrics which allow applications in pattern recognition and visualization. The contributions of the PI were obtained mainly in collaboration with David Mumford. In the paper [M107] via the Hamiltonian approach many metrics were investigated, together with their conserved quantities (one of them is the reparameterization momentum) and their sectional curvatures. Recall from a result of the predecessor of this project, that the L2-metric on the space of immersions has zero geodesic distance on the orbit space under the reparameterization group. These metrics come in 3 flavors: Some are derived from the the L2-metric by multiplying it with a function of the length of the curve (a conformal cha...

Indagationes Mathematicae (Proceedings), 1983

2020

In this research article, Lie Groups and Lie Algebras are projected in a distinct direction and with innovative proofs. We develop the necessary and sufficient condition for a topological group to be Hausdorff. The criteria of topological group and Haussdorff to be connected is also derived. This research article mainly explores the concept of left in variant field and presents an important hypothesis namely ―any Lie group is parallelizable‖ with a very simple accurate logical and analytical reasoning. Moreover this paper covers the impervious of another property namely every one parameter subgroup is an integral curve of some left-invariant vector field.

Applied Mathematics and Computation, 2009

This paper is devoted to show and explain some applications of Lie Theory to solve some problems in Economics and Mathematical Finance. So we put forward and discuss mathematical aspects and approaches for several economic problems which have been previously considered in the literature. Besides we also show our advances on this topic, mentioning some open problems for future research.