Mirror Geometry of Lie Algebras, Lie Groups and Homogeneous Spaces

• Κύριος συγγραφέας: Sabinin, Lev V. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Dordrecht : Springer Netherlands, 2005.
• Σειρά: Mathematics and Its Applications ; 573
• Θέματα: Mathematics.; Group theory.; Topological groups.; Lie groups.; Geometry.; Differential geometry.; Differential Geometry.; Topological Groups, Lie Groups.; Group Theory and Generalizations.

As K. Nomizu has justly noted [K. Nomizu, 56], Differential Geometry ever will be initiating newer and newer aspects of the theory of Lie groups. This monograph is devoted to just some such aspects of Lie groups and Lie algebras. New differential geometric problems came into being in connection with...

Πίνακας περιεχομένων:

• 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 of Motions and Two-Dimensional Immobile Mirrors.