Overview

This book describes a new and original formalism based on mirror symmetries of Lie groups, Lie algebras and Homogeneous spaces. Special systems of mirrors are used for classification purposes and as an instrument for studies of Homogeneous spaces. Tri-symmetric and arbitrary Riemannian Homogeneous spaces can also be researched in this way. The book should be of particular interest to researchers in Lie Groups, Lie Algebras, Differential Geometry and their applications but it should also prove useful for other postgraduate and advanced graduate students in mathematics.

Full Product Details

Author:   Lev V. Sabinin
Publisher:   Springer
Imprint:   Springer
Edition:   1st ed. Softcover of orig. ed. 2004
Volume:   573
Dimensions:   Width: 16.00cm , Height: 1.70cm , Length: 24.00cm
Weight:   0.538kg
ISBN:  

9789048166763

ISBN 10:   9048166764
Pages:   312
Publication Date:   28 October 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

Preliminaries.- Curvature Tensor of an Involutive Pair. Classical Inovolutive Pairs of Index 1.- Iso-Involutive Sums of Lie Algebras.- Iso-Involutive Base and Structure Equations.- Iso-Involutive Sums of Types 1 and 2.- Iso-Involutive Sums of Lower Index 1.- Principal Central Involutive Automorphism of Type U.- Principal Unitary Involutive Automorphism of Index 1.- Hyper-Involutive Decomposition of a Simple Compact Lie Algebra.- Some Auxiliary Results.- Principal Involutive Automorphisms of Type O.- Fundamental Theorem.- Principal Di-Unitary Involutive Automorphism.- Singular Principal Di-Unitary Involutive Automorphism.- Mono-Unitary Non-Central Principal Involutive Automorphism.- Exceptional Principal Involutive Automorphism of Types f and e.- Classification of Simple Special Unitary Subalgebras.- Hyper-Involutive Reconstructions of Basis Involutive Decompositions.- Special Hyper-Involutive Sums.- Notations, Definitions and Some Preliminaries.- Symmetric Spaces of Rank 1.- Principal Symmetric Spaces.- Essentially Special Symmetric Spaces.- Some Theorems on Simple Compact Lie Groups.- Tri-Symmetric and Hyper-Tri-Symmetric Spaces.- Tri-Symmetric Spaces with Exceptional Compact Groups.- Tri-Symmetric Spaces with Groups of Motions SO(n), Sp(n), SU(n).- Subsymmetric Riemannian Homogeneous Spaces.- Subsymmetric Homogeneous Spaces and Lie Algebras.- Mirror Subsymmetric Lie Triplets of Riemannian Type.- Mobile Mirrors. Iso-Involutive Decompositions.- Homogeneous Riemannian Spaces with Two-Dimensional Mirrors.- Homogeneous Riemannian Spaces with Groups SO(n), SU(3) and Two-Dimensional Mirrors.- Homogeneous Riemannian Spaces with Simple Compact Lie Groups of Motions G?SO(n), SU(3) and Two-dimensional Mirrors.- Homogeneous Riemannian Spaces with Simple Compact Lie Groups ofMotions and Two-Dimensional Immobile Mirrors.

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