Most cited papers in Advanced Operator Algebra Research
What are the most cited papers in Advanced Operator Algebra Research?
The most cited paper in Advanced Operator Algebra Research is "On the generators of quantum dynamical semigroups" (Göran Lindblad, 1976), with 7,738 citations. Next come "String theory and noncommutative geometry" (3,743) and "Completely positive linear maps on complex matrices" (2,767).
Showing 50 of 99 papers. Every paper with more than 404 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | On the generators of quantum dynamical semigroups Göran Lindblad · Communications in Mathematical Physics | Jun 1976 | 7,738 |
| 2 | String theory and noncommutative geometry Nathan Seiberg, Edward Witten · Journal of High Energy Physics | 30 Sep 1999 | 3,743 |
| 3 | Completely positive linear maps on complex matrices Man-Duen Choi · Linear Algebra and its Applications | Jun 1975 | 2,767 |
| 4 | Noncommutative Geometry Alain Connes, Joachim Cuntz, Marc A. Rieffel · Oberwolfach Reports | 30 Jun 2010 | 2,326 |
| 5 | The “transition probability” in the state space of a ∗-algebra Armin Uhlmann · Reports on Mathematical Physics | Apr 1976 | 1,691 |
| 6 | Invariants of 3-manifolds via link polynomials and quantum groups Nicolai Reshetikhin, Vladimir Georgievich Turaev · Inventiones mathematicae | Dec 1991 | 1,589 |
| 7 | Noncommutative geometry and Matrix theory Alain Connes, Michael R. Douglas, Albert S. Schwarz · Journal of High Energy Physics | 5 Feb 1998 | 1,355 |
| 8 | Noncommutative Geometry and Matrix Theory: Compactification on Tori Alain Connes, Michael R. Douglas, Albert S. Schwarz · arXiv (Cornell University) | 20 Nov 1997 | 1,310 |
| 9 | SimpleC*-algebra generated by isometries Joachim Cuntz · Communications in Mathematical Physics | Jun 1977 | 1,291 |
| 10 | Non-commutative differential geometry Alain Connes · Publications mathématiques de l IHÉS | 7 Dec 1985 | 1,272 |
| 11 | A new polynomial invariant of knots and links Peter J. Freyd, David N. Yetter, Jim Hoste et al. · Bulletin of the American Mathematical Society | 1985 | 1,230 |
| 12 | Quantum Ito's formula and stochastic evolutions R. L. Hudson, Kalyanapuram Rangachari Parthasarathy · Communications in Mathematical Physics | Sep 1984 | 1,228 |
| 13 | Subalgebras of C*-algebras William Arveson · Acta Mathematica | 1969 | 1,177 |
| 14 | Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops Vasily Pestun · Communications in Mathematical Physics | 21 May 2012 | 1,171 |
| 15 | Differential calculus on compact matrix pseudogroups (quantum groups) Stanisław Lech Woronowicz · Communications in Mathematical Physics | Mar 1989 | 1,137 |
| 16 | 1 USER-FRIENDLY TAIL BOUNDS FOR SUMS OF RANDOM MATRICES Joel A. Tropp | Apr 2010 | 1,068 |
| 17 | An SU(2) anomaly Edward H. Witten · Physics Letters B | Nov 1982 | 1,034 |
| 18 | EquivariantKK-theory and the Novikov conjecture Gennadi Kasparov · Inventiones mathematicae | Feb 1988 | 955 |
| 19 | A class ofC *-algebras and topological Markov chains Joachim Cuntz, Wolfgang Krieger · Inventiones mathematicae | Oct 1980 | 922 |
| 20 | Aspects of the functional renormalisation group Jan M. Pawlowski · Annals of Physics | 22 Jan 2007 | 898 |
| 21 | Foliations and the topology of 3-manifolds David Gabai · Journal of Differential Geometry | 1983 | 898 |
| 22 | λ1, Isoperimetric inequalities for graphs, and superconcentrators Noga Alon, Vitali Davidovich Milman · Journal of Combinatorial Theory Series B | Feb 1985 | 878 |
| 23 | Quantum theory of geometry: I. Area operators Abhay Ashtekar, Jerzy Lewandowski · Classical and Quantum Gravity | 1997 | 862 |
| 24 | Twisted $\textit{SU}(2)$ Group. An Example of a Non-Commutative Differential Calculus Stanisław Lech Woronowicz · Publications of the Research Institute for Mathematical Sciences | 28 Feb 1987 | 852 |
| 25 | Loop space representation of quantum general relativity Carlo Rovelli, Lee Smolin · Nuclear Physics B | Feb 1990 | 845 |
| 26 | On quantum gauge theories in two dimensions Edward H. Witten · Communications in Mathematical Physics | Oct 1991 | 838 |
| 27 | Hopf Algebras, Renormalization and Noncommutative Geometry Alain Connes, Dirk Kreimer · Communications in Mathematical Physics | Dec 1998 | 837 |
| 28 | Limit laws for Random matrices and free products Dan Voiculescu · Inventiones mathematicae | Dec 1991 | 827 |
| 29 | Bicrossproduct structure of κ-Poincare group and non-commutative geometry Shahn Majid, H. Ruegg · Physics Letters B | Aug 1994 | 817 |
| 30 | Induced representations of C∗-algebras Marc A. Rieffel · Advances in Mathematics | Jun 1974 | 746 |
| 31 | Banach spaces related to integrable group representations and their atomic decompositions, I Hans Georg Feichtinger, Karlheinz Gröchenig · Journal of Functional Analysis | Oct 1989 | 730 |
| 32 | Generalizeds-numbers ofτ-measurable operators Thierry Fack, Hideki Kosaki · Pacific Journal of Mathematics | Jun 1986 | 717 |
| 33 | Spectral asymmetry and Riemannian geometry. III Michael Francis Atiyah, V. K. Patodi, I. M. Singer · Mathematical Proceedings of the Cambridge Philosophical Society | 1976 | 687 |
| 34 | Completely positive maps and entropy inequalities Göran Lindblad · Communications in Mathematical Physics | Jun 1975 | 686 |
| 35 | The Spin-Foam Approach to Quantum Gravity Alejandro Colsa Perez · Living Reviews in Relativity | 14 Feb 2013 | 685 |
| 36 | Planar diagrams, two-dimensional lattice gravity and surface models François David · Nuclear Physics B | 1985 | 684 |
| 37 | Morita Equivalence and Continuous-Trace $C^*$-Algebras Iain Raeburn, Dana P. Williams · CERN Document Server (European Organization for Nuclear Research) | 3 Aug 1998 | 651 |
| 38 | Entropy and isomorphism theorems for actions of amenable groups Donald S. Ornstein, Benjamin Weiss · Journal d Analyse Mathématique | Dec 1987 | 646 |
| 39 | Chern-Simons gauge theory as a string theory Edward H. Witten · Birkhäuser Basel eBooks | 1995 | 627 |
| 40 | C ∗ -algebras associated with irrational rotations Marc A. Rieffel · Pacific Journal of Mathematics | Apr 1981 | 617 |
| 41 | D-branes and the noncommutative torus Michael R Douglas, Chris Hull · Journal of High Energy Physics | 12 Feb 1998 | 611 |
| 42 | Hall algebras and quantum groups Claus Michael Ringel · Inventiones mathematicae | Dec 1990 | 594 |
| 43 | The coarse Baum–Connes conjecture for spaces which admit a uniform embedding into Hilbert space Guoliang Yu · Inventiones mathematicae | 2000 | 582 |
| 44 | Gauge theory on noncommutative spaces J. Madore, S. Schraml, Peter Schupp et al. · The European Physical Journal C | Aug 2000 | 581 |
| 45 | Covariant differential calculus on the quantum hyperplane Julius Wess, Bruno Zumino · Nuclear Physics B - Proceedings Supplements | 1991 | 581 |
| 46 | Moduli of graphs and automorphisms of free groups Marc Culler, Karen Vogtmann · Inventiones mathematicae | Feb 1986 | 578 |
| 47 | On a Lorentz-invariant interpretation of noncommutative space–time and its implications on noncommutative QFT Масуд Чайчиан, Petr Petrovich Kulish, K. Nishijima et al. · Physics Letters B | 5 Nov 2004 | 578 |
| 48 | Quantum theory of geometry II: Volume operators Abhay Ashtekar, Jerzy Lewandowski · Advances in Theoretical and Mathematical Physics | 1997 | 577 |
| 49 | On the structure of manifolds with positive scalar curvature R. Schoen, S.-T. Yau · manuscripta mathematica | 1979 | 577 |
| 50 | Noncommutative geometry and reality Alain Connes · Journal of Mathematical Physics | Nov 1995 | 569 |
Citations are OpenAlex's own counts, from its 2026-09-23 snapshot, so the ranking can differ from Google Scholar or Web of Science. A paper is listed for a field when OpenAlex files it under one of the field's topics; retracted papers and papers whose citation count cannot be traced to citing works are left out, and a preprint and the article it became are shown once. Release dates are OpenAlex's: where a source gave only a month or a year, that is what is shown. How the lists are chosen.