MSc Thesis: Presentation of Certain New Trends in Noncommutative Geometry

Abstract

MSc thesis of the author offering an introduction to the operator algebraic approach to noncommutative geometry, with a treatment of some more advanced elements such as the noncommutative geometry of quantum groups, fuzzy physics, and compact quantum metric spaces.

References in corpus (18)

• Gravity coupled with matter and foundation of non-commutative geometry
• Hopf algebras, cyclic cohomology and the transverse index theory
• Metrics on states from actions of compact groups
• Matrix algebras converge to the sphere for quantum Gromov--Hausdorff distance
• Type III and spectral triples
• Matrix ${\varphi }^4$ Models on the Fuzzy Sphere and their Continuum Limits
• Reconstruction of manifolds in noncommutative geometry
• Towards Finite Quantum Field Theory in Non-Commutative Geometry
• Fuzzy Complex Grassmannian Spaces and their Star Products
• Strict quantization of coadjoint orbits
• An Introduction to K-theory and Cyclic Cohomology
• On Spin Structures and Dirac Operators on the Noncommutative Torus
• Noncommutative Regularization for the Practical Man
• Dualising complexes and twisted Hochschild (co)homology for noetherian Hopf algebras
• The problem of completeness for Gromov-Hausdorff metrics on C*-algebras
• Simulating the scalar field on the fuzzy sphere
• Field Theory Simulations on a Fuzzy Sphere - an Alternative to the Lattice
• Compact quantum metric spaces and ergodic actions of compact quantum groups