Téléchargez le livre : Quantum Riemannian Geometry

Quantum Riemannian Geometry

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Éditeur :

Springer


Collection :

Grundlehren der mathematischen Wissenschaften

Paru le : 2020-01-31

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Description

This book provides a comprehensive account of a modern generalisation of differential geometry in which coordinates need not commute. This requires a reinvention of differential geometry that refers only to the coordinate algebra, now possibly noncommutative, rather than to actual points.
Such a theory is needed for the geometry of Hopf algebras or quantum groups, which provide key examples, as well as in physics to model quantum gravity effects in the form of quantum spacetime. The mathematical formalism can be applied to any algebra and includes graph geometry and a Lie theory of finite groups. Even the algebra of 2 x 2 matrices turns out to admit a rich moduli of quantum Riemannian geometries. The approach taken is a `bottom up’ one in which the different layers of geometry are built up in succession, starting from differential forms and proceeding up to the notion of a quantum `Levi-Civita’ bimodule connection, geometric Laplacians and, in some cases, Dirac operators. Thebook also covers elements of Connes’ approach to the subject coming from cyclic cohomology and spectral triples. Other topics include various other cohomology theories, holomorphic structures and noncommutative D-modules.
A unique feature of the book is its constructive approach and its wealth of examples drawn from a large body of literature in mathematical physics, now put on a firm algebraic footing. Including exercises with solutions, it can be used as a textbook for advanced courses as well as a reference for researchers.
Pages
809 pages
Collection
Grundlehren der mathematischen Wissenschaften
Parution
2020-01-31
Marque
Springer
EAN papier
9783030302931
EAN PDF
9783030302948
Informations sur l'ebook
Nombre pages copiables
8
Nombre pages imprimables
80
Taille du fichier
15022 Ko
Prix
94,94 €

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