World Library  

QR link for An Introduction to Noncommutative Spaces and Their Geometry
Add to Book Shelf
Flag as Inappropriate
Email this Book

An Introduction to Noncommutative Spaces and Their Geometry

By Landi, Giovanni

Click here to view

Book Id: WPLBN0000659371
Format Type: PDF eBook
File Size: 1.33 MB
Reproduction Date: 2005

Title: An Introduction to Noncommutative Spaces and Their Geometry  
Author: Landi, Giovanni
Volume:
Language: English
Subject: Science., Mathematics, Logic
Collections:
Historic
Publication Date:
Publisher:

Citation

APA MLA Chicago

Landi, G. (n.d.). An Introduction to Noncommutative Spaces and Their Geometry. Retrieved from http://community.worldlibrary.net/


Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: These notes arose from a series of introductory seminars on noncommutative geometry I gave at the University of Trieste in September 1995 during the XWorkshop on Differential GeometricMethods in Classical Mechanics. It was Beppe Marmo's suggestion that I wrote notes of the lectures. The notes are mainly an introduction to Connes' noncommutative geometry. They could serve as a ` rst aid kit' before one ventures into the beautiful but bewildering landscape of Connes' theory [25]. The main di erence with other available introductions to Connes's work, notably Kastler's papers [65] and also Gracia-Bond a and Varilly paper [101], is the emphasis on noncommutative spaces seen as concrete spaces.

Table of Contents
Contents 1 Introduction 1 2 Noncommutative Spaces and Algebras of Functions 5 2.1 Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Commutative Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Noncommutative Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.1 The Jacobson (or hull-kernel)Topology . . . . . . . . . . . . . . . . 12 2.4 Compact Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3 Noncommutative Lattices 19 3.1 The Topological Approximation . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2 Order and Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 How to Recover the Space BeingApproximated . . . . . . . . . . . . . . . 26 3.4 Noncommutative Lattices . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.1 The space PrimA as a Poset . . . . . . . . . . . . . . . . . . . . . 33 3.4.2 AF-Algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4.3 From Bratteli Diagrams to Noncommutative Lattices . . . . . . . . 40 3.4.4 From Noncommutative Lattices to Bratteli Diagrams . . . . . . . . 43 3.5 How to Recover the Algebra BeingApproximated . . . . . . . . . . . . . . 54 3.6 Operator Valued Functions on Noncommutative Lattices . . . . . . . . . . 55 4 Modules as Bundles 57 4.1 Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 ProjectiveModules of Finite Type . . . . . . . . . . . . . . . . . . . . . . . 59 4.3 Hermitian Structures over ProjectiveModules . . . . . . . . . . . . . . . . 62 4.4 Few Elements of K-theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4.1 The Group K0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4.2 The K-theory of the Penrose Tiling . . . . . . . . . . . . . . . . . . 68 4.4.3 Higher Order K-groups . . . . . . . . . . . . . . . . . . . . . . . . . 72 5 The Spectral Calculus 75 5.1 In nitesimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

 

Click To View

Additional Books


  • Determination of Lithium (by )
  • Curious Facts in the History of Insects;... (by )
  • Applied Thermodynamics for Engineers (by )
  • Zbirka Tvoriv Ukraïnskykh Pysmennykiv 
  • New Methods in Analytical Chemistry (by )
  • Algebra-Russian (by )
  • Animal Breeding Plans (by )
  • The Point of View (by )
  • The Pension Beaurepas (by )
  • The Patagonia (by )
  • The Papers (by )
  • The Papers (by )
Scroll Left
Scroll Right

 



Copyright © World Library Foundation. All rights reserved. eBooks from World Library are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.