2006/12/04 by Thierry Masson, Masson, Thierry · 1 citation
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.math-ph/0612012
openalex publication_date 2006/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This informal introduction is an extended version of a three hours lecture given at the 6th Peyresq meeting ``Integrable systems and quantum field theory''. In this lecture, we make an overview of some of the mathematical results which motivated the development of what is called noncommutative geometry. The first of these results is the theorem by Gelfand and Neumark about commutative C^∗-algebras; then come some aspects of the K-theories, first for topological spaces, then for C^∗-algebras and finally the purely algebraic version. Cyclic homology is introduced, keeping in mind its relation to differential structures. The last result is the construction of the Chern character, which shows how these developments are related to each other.