Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

The Guest Editors for this special issue are

George Elliott (University of Toronto, Canada)
Piotr M. Hajac (Institute of Mathematics of Polish Academy of Sciences, Poland)
Hanfeng Li (University at Buffalo, USA)
Jonathan Rosenberg (University of Maryland, USA)

This special issue is a tribute to Marc A. Rieffel, marking (approximately) his 75th birthday. It is the outgrowth of a Focus Program on Noncommutative Geometry and Quantum Groups that took place at the Fields Institute for Research in Mathematical Sciences in Toronto, Canada, in June, 2013. Marc Rieffel has been one of the most influential researchers in the world in the areas of noncommutative geometry and quantum groups. He has had over 30 PhD students and over 80 “mathematical descendants”. Among his major contributions were the introduction of Morita equivalence as a fundamental notion in noncommutative geometry and the classification of C*-algebras, the introduction of stable rank as a basic invariant of C*-algebras, the introduction of strict deformation quantization to construct new examples of quantum groups, and the analysis of the metric structure of noncommutative geometries. The papers in this special issue reflect the wide range of his contributions to mathematics as well as the great esteem in which he is held by the world mathematical community.

The Guest Editors        

Papers in this Issue:

Generalized Coefficients for Hopf Cyclic Cohomology
Mohammad Hassanzadeh, Dan Kucerovsky and Bahram Rangipour
SIGMA 10 (2014), 093, 16 pages   [ abs   pdf ]
Piecewise Principal Coactions of Co-Commutative Hopf Algebras
Bartosz Zieliński
SIGMA 10 (2014), 088, 20 pages   [ abs   pdf ]
Locally Compact Quantum Groups. A von Neumann Algebra Approach
Alfons Van Daele
SIGMA 10 (2014), 082, 41 pages   [ abs   pdf ]
Quantitative K-Theory Related to Spin Chern Numbers
Terry A. Loring
SIGMA 10 (2014), 077, 25 pages   [ abs   pdf ]
Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles
Debashish Goswami and Soumalya Joardar
SIGMA 10 (2014), 076, 18 pages   [ abs   pdf ]
Big Bang, Blowup, and Modular Curves: Algebraic Geometry in Cosmology
Yuri I. Manin and Matilde Marcolli
SIGMA 10 (2014), 073, 20 pages   [ abs   pdf ]
Groupoid Actions on Fractafolds
Marius Ionescu and Alex Kumjian
SIGMA 10 (2014), 068, 14 pages   [ abs   pdf ]
Non-Commutative Resistance Networks
Marc A. Rieffel
SIGMA 10 (2014), 064, 46 pages   [ abs   pdf ]
Local Proof of Algebraic Characterization of Free Actions
Paul F. Baum and Piotr M. Hajac
SIGMA 10 (2014), 060,  7 pages   [ abs   pdf ]
Induced Representations and Hypergroupoids
Jean Renault
SIGMA 10 (2014), 057, 18 pages   [ abs   pdf ]
Ordered *-Semigroups and a C*-Correspondence for a Partial Isometry
Berndt Brenken
SIGMA 10 (2014), 055, 50 pages   [ abs   pdf ]
The Classification of All Crossed Products H4#k[Cn]
Ana-Loredana Agore, Costel-Gabriel Bontea and Gigel Militaru
SIGMA 10 (2014), 049, 12 pages   [ abs   pdf ]
Nontrivial Deformation of a Trivial Bundle
Piotr M. Hajac and Bartosz Zieliński
SIGMA 10 (2014), 031,  7 pages   [ abs   pdf ]
On Projections in the Noncommutative 2-Torus Algebra
Michał Eckstein
SIGMA 10 (2014), 029, 14 pages   [ abs   pdf ]
The Structure of Line Bundles over Quantum Teardrops
Albert Jeu-Liang Sheu
SIGMA 10 (2014), 027, 11 pages   [ abs   pdf ]
On the Smoothness of the Noncommutative Pillow and Quantum Teardrops
Tomasz Brzeziński
SIGMA 10 (2014), 015,  8 pages   [ abs   pdf ]
Exploring the Causal Structures of Almost Commutative Geometries
Nicolas Franco and Michał Eckstein
SIGMA 10 (2014), 010, 23 pages   [ abs   pdf ]
The Heisenberg Relation - Mathematical Formulations
Richard V. Kadison and Zhe Liu
SIGMA 10 (2014), 009, 40 pages   [ abs   pdf ]
Representation Theory of Quantized Enveloping Algebras with Interpolating Real Structure
Kenny De Commer
SIGMA 9 (2013), 081, 20 pages   [ abs   pdf ]
Levi-Civita's Theorem for Noncommutative Tori
Jonathan Rosenberg
SIGMA 9 (2013), 071,  9 pages   [ abs   pdf ]

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