| 书目名称 | Quantum Riemannian Geometry | | 编辑 | Edwin J. Beggs,Shahn Majid | | 视频video | | | 概述 | Provides a self-contained and constructive approach to noncommutative differential geometry, which connects to the earlier approach to noncommutative geometry of Alain Connes in a complementary way.Co | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | .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 noncommutativ | | 出版日期 | Book 2020 | | 关键词 | noncommutative geometry; quantum groups; Hopf algebra; differential graded algebra; quantum Levi-Civita | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-030-30294-8 | | isbn_softcover | 978-3-030-30296-2 | | isbn_ebook | 978-3-030-30294-8Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer Nature Switzerland AG 2020 |
The information of publication is updating
|
|
发表于 2025-3-21 16:16:45
