TAILIEUCHUNG - Basic Noncommutative Geometry

One of the major advances of science in the 20th century was the discovery of a mathematical formulation of quantum mechanics by Heisenberg in 1925 [94].1 From a mathematical point of view, this transition from classical mechanics to quantum mechanics amounts to, among other things, passing from the commutative algebra of classical observables to the noncommutative algebra of quantum mechanical observables. To understand this better we recall that in classical mechanics an observable of a system (. energy, position, momentum, etc.) is a function on a manifold called the phase space of the system. Classical observables can therefore be multiplied in a pointwise manner and this multiplication is. | EMS Series of Lectures in Mathematics Edited by Andrew Ranicki University of Edinburgh . EMS Series of Lectures in Mathematics is a book series aimed at students professional mathematicians and scientists. It publishes polished notes arising from seminars or lecture series in all fields of pure and applied mathematics including the reissue of classic texts of continuing interest. The individual volumes are intended to give a rapid and accessible introduction into their particular subject guiding the audience to topics of current research and the more advanced and specialized literature. Previously published in this series Katrin Wehrheim Uhlenbeck Compactness Torsten Ekedahl One Semester of Elliptic Curves Sergey V. Matveev Lectures on Algebraic Topology Joseph C. Várilly An Introduction to Noncommutative Geometry Reto Muller Differential Harnack Inequalities and the Ricci Flow Eustasio del Barrio Paul Deheuvels and Sara van de Geer Lectures on Empirical Processes Iskander A. Taimanov Lectures on Differential Geometry Martin J. Mohlenkamp María Cristina Pereyra Wavelets Their Friends and What They Can Do for You Stanley E. Payne and Joseph A. Thas Finite Generalized Quadrangles Masoud Khalkhali Basic Noncommutative Geometry uropean athematical .

• Y học thường thức
• Noncommutative quotients
• Equivalence of categories
• Gelfand–Naimark theorems
• Projective modules
• Connes–Chern character
• Cyclic cohomology