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Saturday, May 16, 2020 | History

5 edition of Infinite dimensional Lie groups in geometry and representation theory found in the catalog.

Infinite dimensional Lie groups in geometry and representation theory

Washington, DC, USA 17-21 August 2000

  • 35 Want to read
  • 3 Currently reading

Published by World Scientific in River Edge, N.J .
Written in English

    Subjects:
  • Lie groups -- Congresses.,
  • Infinite groups -- Congresses.,
  • Infinite dimensional Lie algebras -- Congresses.,
  • Infinite-dimensional manifolds -- Congresses.

  • Edition Notes

    Includes bibliographical references.

    Statementeditors, Augustia Banyaga, Joshua A. Leslie, Theirry Robart.
    GenreCongresses.
    ContributionsBanyaga, Augustin., Leslie, Joshua A. 1933-, Robart, Thierry P., 1963-
    Classifications
    LC ClassificationsQA387 .I567 2002
    The Physical Object
    Paginationix, 163 p. ;
    Number of Pages163
    ID Numbers
    Open LibraryOL3438872M
    ISBN 10981238068X
    LC Control Number2005297938
    OCLC/WorldCa50705543

    Beyond the techniques and ideas related to representation theory, the book demonstrates connections to number theory, algebraic geometry, and mathematical physics. Specific topics covered include Hecke algebras, quantum groups, infinite-dimensional Lie algebras, quivers, modular representations, and Gromov-Witten invariants. Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the groups in question are realized as geometric symmetries or continuous transformations of some spaces).

    A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this paper we show that a pro-Lie group G is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if G is locally contractible. We also characterize the corresponding pro-Lie algebras in various by: Lectures on Lie Algebras (PDF 36P) This is a lecture note for beginners on representation theory of semisimple finite dimensional Lie algebras. It is shown how to use infinite dimensional representations to derive the Weyl character formula. Author(s): Joseph Bernstein.

    MATH b, Quantum Geometry of Moduli Spaces of Local Systems and Representation Theory Alexander Goncharov. The goal of the course is to study character varieties as well as several closely related moduli spaces, assigned to a split semi-simple algebraic group G and a decorated topological surface S. In addition to the traditional “instructional” workshop preceding the conference, there were also workshops on “Commutative Algebra, Algebraic Geometry and Representation Theory”, “Finite Dimensional Algebras, Algebraic Groups and Lie Theory”, and .


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Infinite dimensional Lie groups in geometry and representation theory Download PDF EPUB FB2

It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory.

The book should be a new source of. This volume of proceedings explores infinite dimensional Lie groups in geometry and representation theory.

It treats among other topics the integrability problem of various infinite dimensional Lie algebras, and presents contributions to important subjects in modern geometry. This book constitutes the proceedings of the Howard conference on “Infinite Dimensional Lie Groups in Geometry and Representation Theory”.

It presents some important recent developments in this area. It opens with a topological characterizati. The analytic representation theory of infinite-dimensional Lie groups is still very much underdeveloped.

The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach–Lie–Poisson spaces, and infinite-dimensional generalizations of reductive Lie groups. 's areas of research are infinite-dimensional Lie groups, integrable systems, Poisson geometry, and topological hydrodynamics.

Together with Vladimir Arnold he is the author of the monograph on "Topological methods in hydrodynamics", which has become a standard reference in mathematical fluid dynamics.

The fundamental role played by the theory of Lie groups in mathematical physics, particularly in quantum mechanics and quantum field theory, is due to the presence of a group of symmetries (at least approximately) in the fundamental equations of this theory.

Infinite-dimensional representation. Encyclopedia of Mathematics. In this paper we outline results on orbifold diffeomorphism groups that were presented at the International Conference on Infinite Dimensional Lie Groups in Geometry and Representation Theory at Howard University, Washington DC on AugustSpecifically, we define the notion of reduced and unreduced orbifold diffeomorphism groups.

Introduction to Lie Algebras and Representation Theory so readers interested in Lie algebras over prime characteristic or infinite-dimensional Lie algebras (such as arise in high energy physics), will have to look elsewhere. such as the connection of the theory with Lie groups, and Lie algebras are defined as vector spaces over fields Cited by: Lie Theory: Lie Algebras and Representations contains J.

Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." Both are comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations.

In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact.

Get this from a library. Infinite dimensional Lie groups in geometry and representation theory: Washington, DC, USA August [Augustin Banyaga; Joshua A Leslie; Thierry P Robart;] -- This volume constitutes the proceedings of the Howard conference on "Infinite Dimensional Lie Groups in Geometry and Representation Theory", and presents some.

Lie Groups Beyond an Introduction takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and by: dimensional Lie groups and their applications, mostly in Hamiltonian me-chanics, fluid dynamics, integrable systems, and complex geometry.

We have chosen to present the unifying ideas of the theory by concentrating on specific types and examples of infinite-dimensional Lie groups. Of course, the selection. This book contains written versions of the lectures given at the PCMI Graduate Summer School on the representation theory of Lie groups.

The volume begins with lectures by A. Knapp and P. Trapa outlining the state of the subject around the yearspecifically, the fundamental results of Harish-Chandra on the general structure of infinite-dimensional representations and the.

affine connection assume B-space bundle homomorphism C N(d called compact computation consider construct contact algebra continuous linear mapping converges coordinate system Corollary defined definition deformation quantization denote derivative diffeomorphism differential equation differential operator easy element exponential mapping extends.

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory.

Introduction to Finite and Infinite. We give a review of infinite-dimensional Lie groups and algebras and show some applications and examples in mathematical physics.

This includes diffeomorphism groups and their natural subgroups like volume-preserving and symplectic transformations, as well as gauge groups and loop groups.

Applications include fluid dynamics, Maxwell's equations, and plasma by: 6. The theory of infinite-dimensional Lie algebras differs markedly from the theory of finite-dimensional Lie algebras in that the latter possesses powerful classification theo rems, which usually allow one to "recognize" any finite dimensional Lie algebra (over the field of complex or real numbers), i.e., find it in some list.

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory.

Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. Lie Theory: Lie Algebras and Representations contains J. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H.

Neeb's "Infinite Dimensional Groups and their Representations.". springer, This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics.

The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of .source of the power of Lie theory. The basic object mediating between Lie groups and Lie algebras is the one-parameter group.

Just as an abstract group is a coperent system of cyclic groups, a Lie group is a (very) coherent system of one-parameter groups. The purpose of the first two sections, therefore, is to provide.Lie Groups Representation Theory and Symmetric Spaces. This note covers the following topics: Fundamentals of Lie Groups, A Potpourri of Examples, Basic Structure Theorems, Complex Semisimple Lie algebras, Representation Theory, Symmetric Spaces.

Author(s): Wolfgang Ziller.