Topic · Advanced Topics in Algebra
Most cited papers in Advanced Topics in Algebra
What are the most cited papers in Advanced Topics in Algebra?
The most cited paper in Advanced Topics in Algebra is "The Magma Algebra System I: The User Language" (Wieb Bosma, John Cannon, Catherine Playoust, 1997), with 7,465 citations. Next come "Completely positive linear maps on complex matrices" (2,767) and "Aq-difference analogue of U(g) and the Yang-Baxter equation" (2,665).
Showing 50 of 100 papers. Every paper with more than 617 citations is listed.
| # | Paper | ||
|---|---|---|---|
| 1 | The Magma Algebra System I: The User Language Wieb Bosma, John Cannon, Catherine Playoust · Journal of Symbolic Computation | Sep 1997 | 7,465 |
| 2 | Completely positive linear maps on complex matrices Man-Duen Choi · Linear Algebra and its Applications | Jun 1975 | 2,767 |
| 3 | Aq-difference analogue of U(g) and the Yang-Baxter equation Michio Jimbo · Letters in Mathematical Physics | Jul 1985 | 2,665 |
| 4 | Hopf Algebras and Their Actions on Rings Susan Montgomery · Regional conference series in mathematics | 28 Oct 1993 | 2,592 |
| 5 | Deformation Quantization of Poisson Manifolds Maxim L'vovich Kontsevich · Letters in Mathematical Physics | Dec 2003 | 2,463 |
| 6 | Mean value methods in iteration W. Robert Mann · Proceedings of the American Mathematical Society | Jun 1953 | 2,327 |
| 7 | Higher algebraic K-theory: I Daniel G. Quillen · Lecture notes in mathematics | 1973 | 1,984 |
| 8 | Lie superalgebras Victor Gershevich Kac · Advances in Mathematics | Oct 1977 | 1,890 |
| 9 | Current algebra and Wess-Zumino model in two dimensions V.G. Knizhnik, A. B. Zamolodchikov · Nuclear Physics B | Dec 1984 | 1,861 |
| 10 | Cluster algebras I: Foundations Sergey Fomin, Andrei V. Zelevinsky · Journal of the American Mathematical Society | 28 Dec 2001 | 1,745 |
| 11 | The “transition probability” in the state space of a ∗-algebra Armin Uhlmann · Reports on Mathematical Physics | Apr 1976 | 1,691 |
| 12 | Intersection theory on the moduli space of curves and the matrix airy function Maxim L'vovich Kontsevich · Communications in Mathematical Physics | Jun 1992 | 1,600 |
| 13 | Linear transformations which preserve trace and positive semidefiniteness of operators Andrzej Jamiołkowski · Reports on Mathematical Physics | Dec 1972 | 1,588 |
| 14 | On q-analogues of the quantum harmonic oscillator and the quantum group SU(2) q Alan Macfarlane · Journal of Physics A Mathematical and General | 7 Nov 1989 | 1,586 |
| 15 | The quantum group SU q (2) and a q-analogue of the boson operators Lawrence C. Biedenharn · Journal of Physics A Mathematical and General | 21 Sep 1989 | 1,528 |
| 16 | Deformation theory and quantization. I. Deformations of symplectic structures F. Bayen, Mosh� Flato, Christian Frønsdal et al. · Annals of Physics | Mar 1978 | 1,517 |
| 17 | A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation Michio Jimbo · Letters in Mathematical Physics | Apr 1986 | 1,502 |
| 18 | Planar diagrams E. Brézin, C. Itzykson, Giorgio Parisi et al. · Communications in Mathematical Physics | Feb 1978 | 1,483 |
| 19 | Solitons and Infinite Dimensional Lie Algebras Michio Jimbo, Tetsuji Miwa · Publications of the Research Institute for Mathematical Sciences | 31 Dec 1983 | 1,476 |
| 20 | Gauge algebra and quantization Igor Anatol'evich Batalin, G. A. Vilkovisky · Physics Letters B | Jun 1981 | 1,465 |
| 21 | Boundary conditions, fusion rules and the Verlinde formula John Cardy · Nuclear Physics B | Oct 1989 | 1,379 |
| 22 | Classical and quantum conformal field theory Gregory Moore, Nathan Seiberg · Communications in Mathematical Physics | Jun 1989 | 1,376 |
| 23 | The Zero-Divisor Graph of a Commutative Ring David F. Anderson, Philip S. Livingston · Journal of Algebra | Jul 1999 | 1,350 |
| 24 | SimpleC*-algebra generated by isometries Joachim Cuntz · Communications in Mathematical Physics | Jun 1977 | 1,291 |
| 25 | Non-commutative differential geometry Alain Connes · Publications mathématiques de l IHÉS | 7 Dec 1985 | 1,272 |
| 26 | Supergravity Peter van Nieuwenhuizen · Physics Reports | Feb 1981 | 1,207 |
| 27 | Subalgebras of C*-algebras William Arveson · Acta Mathematica | 1969 | 1,177 |
| 28 | The diamond lemma for ring theory George M. Bergman · Advances in Mathematics | Feb 1978 | 1,174 |
| 29 | The moment map and equivariant cohomology Michael Francis Atiyah, R. Bott · Topology | 1984 | 1,140 |
| 30 | Differential calculus on compact matrix pseudogroups (quantum groups) Stanisław Lech Woronowicz · Communications in Mathematical Physics | Mar 1989 | 1,137 |
| 31 | Gauge symmetry and supersymmetry of multiple M2-branes Jonathan Bagger, Neil Lambert · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields | 7 Mar 2008 | 1,132 |
| 32 | Modular invariance of characters of vertex operator algebras Yongchang Zhu · Journal of the American Mathematical Society | 1996 | 1,119 |
| 33 | FUNCTORIAL SEMANTICS OF ALGEBRAIC THEORIES F. William Lawvere · Proceedings of the National Academy of Sciences | Nov 1963 | 1,079 |
| 34 | Groupes réductifs sur un corps local : I. Données radicielles valuées François Bruhat, Jacques Tits · Publications mathématiques de l IHÉS | 7 Dec 1972 | 1,043 |
| 35 | Categories and cohomology theories Graeme B. Segal · Topology | Sep 1974 | 1,022 |
| 36 | Koszul Duality Patterns in Representation Theory Alexander Beilinson, Victor Ginzburg, Wolfgang Soergel · Journal of the American Mathematical Society | 1996 | 1,016 |
| 37 | Unitary representations of the Virasoro and super-Virasoro algebras Peter A. Goddard, Adrian Kent, D. Olive · Communications in Mathematical Physics | Mar 1986 | 988 |
| 38 | Heegner points and derivatives ofL-series Benedict H. Gross, Don Bernard Zagier · Inventiones mathematicae | Jun 1986 | 979 |
| 39 | Finitistic dimension and a homological generalization of semi-primary rings Hyman E. Bass · Transactions of the American Mathematical Society | 1960 | 961 |
| 40 | EquivariantKK-theory and the Novikov conjecture Gennadi Kasparov · Inventiones mathematicae | Feb 1988 | 955 |
| 41 | Tilting theory and cluster combinatorics Aslak Bakke Buan, Bethany Marsh, Markus Reineke et al. · Advances in Mathematics | 20 Aug 2005 | 948 |
| 42 | Remarks on the canonical quantization of the Chern-Simons-Witten theory Shmuel Elitzur, Gregory Martin Moore, A. Schwimmer et al. · Nuclear Physics B | Oct 1989 | 939 |
| 43 | A class ofC *-algebras and topological Markov chains Joachim Cuntz, Wolfgang Krieger · Inventiones mathematicae | Oct 1980 | 922 |
| 44 | HOPF ALGEBRAS AND THE QUANTUM YANG-BAXTER EQUATION Vladimir Drinfeld · Advanced series in mathematical physics | Mar 1990 | 917 |
| 45 | A proof of the Bieberbach conjecture Louis de Branges · Acta Mathematica | 1985 | 916 |
| 46 | Deformation theory and quantization André Lichnerowicz · Lecture notes in physics | 6 Apr 2008 | 907 |
| 47 | Yang-Baxter equation and representation theory: I Petr Petrovich Kulish, Nicolai Reshetikhin, Evgeny Konstantinovich Sklyanin · Letters in Mathematical Physics | Sep 1981 | 906 |
| 48 | Hilbert functions of graded algebras Richard P. Stanley · Advances in Mathematics | Apr 1978 | 898 |
| 49 | Free subgroups in linear groups Jacques Tits · Journal of Algebra | Feb 1972 | 883 |
| 50 | Common structures between finite systems and conformal field theories through quantum groups Vincent Pasquier, Hubert Saleur · Nuclear Physics B | 1990 | 869 |
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.