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"Noncommutative differential geometry."
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Singular integrals in quantum Euclidean spaces
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of
noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for
rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution
kernels. We deduce
eBook
Noncommutative Geometry
The series de Gruyter Studies in Mathematics was founded in 1982 by the late Professor Heinz Bauer and Professor Peter Gabriel. The series publishes monographs and textbooks in mathematics and its applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. Each volume undergoes peer review using a double-blind reviewing process.
eBook
Lectures on fuzzy and fuzzy SUSY physics
Noncommutative geometry provides a powerful tool for regularizing quantum field theories in the form of fuzzy physics. Fuzzy physics maintains symmetries, has no fermion-doubling problem and represents topological features efficiently. These lecture notes provide a comprehensive introduction to the field. Starting with the construction of fuzzy spaces, using the concrete examples of the fuzzy sphere and fuzzy complex projective spaces, the book moves on to discuss the technology of star products on noncommutative R2d and on the fuzzy sphere. Scalar, spinor and gauge field theories as well as extended objects such as monopoles and nonlinear sigma modes are treated in considerable detail. A detailed treatment of the regularization of supersymmetry is given using the techniques of fuzzy physics.
eBook
Topics in algebraic and noncommutative geometry : proceedings in memory of Ruth Michler, July 20-22, 2001, Luminy, France, October 25-28, 2001, Annapolis, Maryland
This book presents the proceedings of two conferences, Resolution des singularites et geometrie non commutative and the Annapolis Algebraic Geometry Conference. Research articles in the volume cover various topics of algebraic geometry, including the theory of Jacobians, singularities, applications to cryptography, and more. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.
eBook
Noncommutative geometry and representation theory in mathematical physics : satellite conference to the Fourth European Congress of Mathematics, July 5-10, 2004, Karlstad University, Karlstad, Sweden
Mathematics provides a language in which to formulate the laws that govern nature. It is a language proven to be both powerful and effective. In the quest for a deeper understanding of the fundamental laws of physics, one is led to theories that are increasingly difficult to put to the test. In recent years, many novel questions have emerged in mathematical physics, particularly in quantum field theory. Indeed, several areas of mathematics have lately become increasingly influential in physics and, in turn, have become influenced by developments in physics. Over the last two decades, interactions between mathematicians and physicists have increased enormously and have resulted in a fruitful cross-fertilization of the two communities.This volume contains the plenary talks from the international symposium on Noncommutative Geometry and Representation Theory in Mathematical Physics held at Karlstad University (Sweden) as a satellite conference to the Fourth European Congress of Mathematics. The scope of the volume is large and its content is relevant to various scientific communities interested in noncommutative geometry and representation theory. It offers a comprehensive view of the state of affairs for these two branches of mathematical physics. The book is suitable for graduate students and researchers interested in mathematical physics.
eBook
Elliptic theory and noncommutative geometry : nonlocal elliptic operators
Noncommutative geometry, which can rightfully claim the role of a philosophy in mathematicalstudies,undertakesto replacegoodoldnotionsofclassicalgeometry (suchas manifolds,vectorbundles, metrics, di?erentiable structures,etc.) by their abstract operator-algebraic analogs and then to study the latter by methods of the theory of operator algebras.
eBook
Blowing up of non-commutative smooth surfaces
This text looks at topics that include: preliminaries on category theory; non-commutative geometry; pseudo-compact rings; Cohen-Macaulay curves embedded in quasi-schemes; derived categories; quantum plane geometry; and non-commutative cubic surfaces.
eBook
Diffeomorphisms and noncommutative analytic torsion
This book is intended for graduate students and research mathematicians working in global analysis and analysis on manifolds
eBook