Keywords:
Lie algebras.
;
Electronic books.
Description / Table of Contents:
Covering important aspects of the theory of unitary representations of nuclear Lie groups, this self-contained reference presents the general theory of energy representations and addresses various extensions of path groups and algebras.;Requiring only a general knowledge of the theory of unitary representations, topological groups and elementary stochastic analysis, Noncommutative Distributions: examines a theory of noncommutative distributions as irreducible unitary representations of groups of mappings from a manifold into a Lie group, with applications to gauge-field theories; describes the energy representation when the target Lie group G is compact; discusses representations of G-valued jet bundles when G is not necessarily compact; and supplies a synthesis of deep results on quasi-simple Lie algebras.;Providing over 200 bibliographic citations, drawings, tables, and equations, Noncommutative Distributions is intended for research mathematicians and theoretical and mathematical physicists studying current algebras, the representation theory of Lie groups, and quantum field theory, and graduate students in these disciplines.
Type of Medium:
Online Resource
Pages:
1 online resource (207 pages)
Edition:
1st ed.
ISBN:
9781482277579
Series Statement:
Chapman and Hall/CRC Pure and Applied Mathematics Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5379154
DDC:
512/.55
Language:
English
Note:
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- Introduction -- Chapter 1 Basic Functional Groups and Lie Algebras -- 1.1 NotationsandPreliminaries -- 1.2 TheLieAlgebrasC (X, G) and D(X, G) -- 1.3 ThcHilbert-SoboIev Lie Algebras W (X, G) -- 1.4 Technical Results About Some Continuous Sums of Operators -- 1.5 The Hausdorff Series On D (X, G) -- 1.6 TheNuclearGroup D (X, G) -- 1.7 The Lie Algebra ? (X, G) -- The Groups C (X, G) -- 1.8 The Hilbert-Sobolev Lie Groups W (X, G) -- 1.9 The Gauge Groups and Their Various Sobolev CompletionsofOrderl -- 1.10 On Some Subgroups of D (X, G) and Related Topics -- References -- Chapter 2 Multiplicative G-Distributions on a Riemannian Manifold -- 2.1 Introduction -- 2.2 Basic Materials for a Theory of G-Distributions on a Riemannian Manifold -- 2.3 The Action of Diff(X) on D (X, G) -- 2.4 A Basic Tool: Representations ofType (S) -- 2.5 Nonlocated Multiplicative G-Integrals -- The Continuous Tensor Products of Representations of G -- 2.6 The Case Where G Is a Nilpotent Lie Group -- References -- Chapter 3 The Energy Representations of Gauge Groups -- 3.1 Introduction -- 3.2 The Basic Energy Representation Associated with a Riemannian Flag -- 3.3 The Representation U and Its Spectral Measure -- 3.4 T-Property -- T-Property -- 3.5 On the Irreducibility ofthe Basic Energy Representation UF -- 3.6 Rings of Generalized Energy Representations -- References -- Chapter 4 Energy Representations ofPath Groups -- 4.1 Introduction -- 4.2 Standard Brownian Measure on Path Spaces -- 4.3 Reduction ofthe Energy Representation -- 4.4 Irreducibility of Almost All Ua's and Properties of the Right and Left Versions Ur, UE of the Energy Representation -- 4.5 Comments on Further Developments -- References -- Chapter 5 The Algebraic Level: Representations of Current Algebras -- 5.1 Introduction.
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5.2 Affine KAC-Moody Algebras -- 5.3 Some Connected Problems and Applications -- 5.4 Beyond Affine Lie Algebras -- References -- Index.
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