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 ...
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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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Add this copy of An Introduction to Noncommutative Spaces and Their to cart. $112.72, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2014 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
2014, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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2014, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of An Introduction to Noncommutative Spaces and Their to cart. $141.33, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 2014 by Springer.
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2014, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
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2014, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Add this copy of An Introduction to Noncommutative Spaces and Their to cart. $152.60, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1997 by Springer Verlag.
Add this copy of An Introduction to Noncommutative Spaces and Their to cart. $167.70, new condition, Sold by Just one more Chapter rated 3.0 out of 5 stars, ships from Miramar, FL, UNITED STATES, published 1997 by Springer.
Add this copy of An Introduction to Noncommutative Spaces and Their to cart. $189.11, new condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1997 by Springer Verlag.
