Marc Aristide Rieffel is a mathematician noted for his fundamental contributions to C*-algebra[1] and quantum group theory.[2] He is currently a professor in the department of mathematics at the University of California, Berkeley.
Marc Rieffel | |
|---|---|
 | |
| Born | Marc Rieffel December 22, 1937 |
| Nationality | American |
| Alma mater | Columbia University |
| Known for | Noncommutative torus |
| Scientific career | |
| Fields | C*-algebras Quantum group theory Noncommutative geometry |
| Institutions | University of California, Berkeley |
| Doctoral advisor | Richard Kadison |
| Doctoral students | Philip Green Jonathan Rosenberg |
In 2012, he was selected as one of the inaugural fellows of the American Mathematical Society.[3]
Contributions edit
Rieffel earned his doctorate from Columbia University in 1963 under Richard Kadison with a dissertation entitled A Characterization of Commutative Group Algebras and Measure Algebras.
Rieffel introduced Morita equivalence as a fundamental notion in noncommutative geometry and as a tool for classifying C*-algebras.[1] For example, in 1981 he showed that if Aθ denotes the noncommutative torus of angle θ, then Aθ and Aη are Morita equivalent if and only if θ and η lie in the same orbit of the action of SL(2, Z) on R by fractional linear transformations.[4] More recently, Rieffel has introduced a noncommutative analogue of Gromov-Hausdorff convergence for compact metric spaces which is motivated by applications to string theory.[5]
References edit
- ^ a b G Cortinas (2008) K-theory and Noncommutative Geometry, European Mathematical Society.
- ^ Symmetry, Integrability and Geometry: Methods and Applications (2014) vol 10; Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel.
- ^ List of Fellows of the American Mathematical Society, retrieved 2014-03-17.
- ^ Rieffel, Marc A. (1981). "C*-Algebras Associated with Irrational Rotations" (PDF). Pacific Journal of Mathematics. 93 (2): 415–429 [416]. doi:10.2140/pjm.1981.93.415. Retrieved 28 February 2013.
- ^ Rieffel, Marc A. (2004). "Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance" (PDF). Memoirs of the American Mathematical Society. doi:10.1090/memo/0796. S2CID 10059366. Retrieved 17 December 2019.