An introduction to noncommutative spaces and their geometries / Giovanni Landi
- 作者： Landi, Giovanni.
- 其他作者：
- 其他題名：
- Springer e-books
- 出版： Berlin ;New York : Springer c1997
- 叢書名： Lecture notes in physics.. New series m, Monographs ,m51
- 主題： Algebraic spaces. , Noncommutative differential geometry.
- ISBN： 9783540635093 (paper)
- URL：
電子書
-
讀者標籤：
- 系統號： 005166477 | 機讀編目格式
館藏資訊
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.
