nLab Marc Rieffel

• webpage

Selected writings

On the Stone-von Neumann theorem:

• Marc Rieffel, On the uniqueness of the Heisenberg commutation relations, Duke Math. J. 39 4 (1972) 745-752 [doi:10.1215/S0012-7094-72-03982-8]

On noncommutative tori:

• Marc A. Rieffel, $C^\ast$-algebras associated with irrational rotations, Pacific Journal of Mathematics 93:2 (1981), 415–429 (pdf, doi:10.2140/pjm.1981.93.415, euclid:pjm/1102736269)

• Marc A. Rieffel: Non-Commutative Tori – A Case Study on Non-Commutative Differentiable Manifolds, in Geometric and Topological Invariants of Elliptic Operators, Contemporary Mathematics 105, AMS (1990) 191-211 [doi:10.1090/conm/105, pdf]

• Marc Rieffel, Albert Schwarz, Morita equivalence of multidimensional noncommutative tori, Int. J. Math. 10 (1999) 289-299 (arXiv:math/9803057)

Introducing the notion of C-star algebraic deformation quantization (strict deformation quantization):

• Marc A. Rieffel, Deformation quantization of Heisenberg manifolds, Communications in Mathematical Physics 122 (1989) 531–562 [doi:10.1007/BF01256492]

• Marc Rieffel, Deformation quantization and operator algebras, in: Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988), 411-423, Proc. Sympos. Pure Math. 51, Part 1, Amer. Math. Soc. (1990) [pdf, pdf MR91h:46120]

• Marc Rieffel, Deformation quantization for actions of $\mathbb{R}^d$, Mem. Amer. Math. Soc. 106 506 (1993) [ams:memo-106-506, MR94d:46072]

• Marc Rieffel, Quantization and $C^\ast$-algebras, Contemporary Mathematics 167 (1994) [pdf, pdf]

Specifically on Lie-group algebras as strict deformation quantization of Lie-Poisson structures:

• Marc A. Rieffel, Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures, American Journal of Mathematics 112 4 (1990) 657-685 [doi:10.2307/2374874, jstor:2374874]

Review with open questions:

• Marc Rieffel, Questions on quantization, Contemp. Math. 228 (1998) 315-326 [arXiv:quant-ph/9712009]

Related entries

• C-star algebraic deformation quantization

category: people