An Introduction to Noncommutative Spaces and their Geometry by Giovanni Landi - PDF
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About this book :-
This book explains a new kind of geometry called noncommutative geometry. In regular geometry, the order in which you multiply coordinates doesn’t matter (for example, 2 × 3 is the same as 3 × 2). But in noncommutative geometry, this is not true, the order can change the result. This idea is important in physics and math, especially in quantum theory. The book starts by explaining why this new kind of geometry is useful. Then it shows how spaces can be studied by looking at the functions on them, and how this idea can be extended to noncommutative cases.
It also explains how familiar ideas like vector bundles (which you can think of as collections of vectors attached to every point in space) can be understood in this new setting.
The book covers how to do calculus and understand shapes and curvature in these noncommutative spaces. It gives examples, like special noncommutative shapes called noncommutative tori, and introduces more advanced ideas used by researchers. This book is good for students and researchers who want to understand the basics of noncommutative geometry.
Book Detail :-
This book has following details information.
Title:
An Introduction to Noncommutative Spaces and their Geometry by Giovanni Landi - PDF
Publisher:
arXiv
Year:
1997
Pages:
186
Type:
PDF
Language:
English
ISBN-10 #:
354014949X
ISBN-13 #:
978-3540149491
License:
N\A
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About Author :-
The author NA
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Book Contents :-
This book has following table of contents.
1. Introduction
2. Noncommutative Spaces and Algebras of Functions
3. Noncommutative Lattices
4. Modules as Bundles
5. The Spectral Calculus
6. Noncommutative Differential Forms
7. Connections on Modules
8. Field Theories on Modules
9. Gravity Models
10. Quantum Mechanical Models on Noncommutative Lattices
A. Basic Notions of Topology
B. The Gel’fand-Naimark-Segal Construction
C. Hilbert Modules
D. Strong Morita Equivalence
E. Partially Ordered Sets
F. Pseudodifferential Operators
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