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Sinopsis
These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content. This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.
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These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.
Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.
Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.
This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.
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An Introduction to Noncommutative Spaces and Their Geometries
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book is a comprehensible introduction for physicists to A. Connes approach to noncommutative geometry.These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative. Nº de ref. del artículo: 5222388
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Introduction to Noncommutative Spaces and Their Geometries
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An Introduction to Noncommutative Spaces and Their Geometries
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ISBN 10: 3662141094
ISBN 13: 9783662141090
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Taschenbuch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'\*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics. 224 pp. Englisch. Nº de ref. del artículo: 9783662141090
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An Introduction to Noncommutative Spaces and Their Geometries
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Springer Berlin Heidelberg, 2014
ISBN 10: 3662141094
ISBN 13: 9783662141090
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Taschenbuch. Condición: Neu. Druck auf Anfrage Neuware - Printed after ordering - These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'\*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics. Nº de ref. del artículo: 9783662141090
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An Introduction to Noncommutative Spaces and Their Geometries (Lecture Notes in Physics Monographs)
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An Introduction to Noncommutative Spaces and Their Geometries
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Taschenbuch. Condición: Neu. Neuware -These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'\*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content. This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 224 pp. Englisch. Nº de ref. del artículo: 9783662141090
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An Introduction to Noncommutative Spaces and Their Geometries
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ISBN 10: 3662141094
ISBN 13: 9783662141090
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Condición: New. Series: Lecture Notes in Physics Monographs (Closed). Num Pages: 222 pages, biography. BIC Classification: PBMP; PHD; PHU. Category: (P) Professional & Vocational. Dimension: 235 x 155 x 12. Weight in Grams: 349. . 2014. Paperback. . . . . Nº de ref. del artículo: V9783662141090
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An Introduction to Noncommutative Spaces and Their Geometries
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