Science Explorer Back to mapMap
Discussion
Topic · Mathematical Physics

Advanced Operator Algebra Research

Advanced Operator Algebra Research is a research topic within Mathematical Physics. Science Explorer counts 15k research works in it since 1951. 10.1% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the classification, properties, and applications of C*-algebras, including topics such as quantum groups, noncommutative geometry, K-theory, locally compact groups, von Neumann algebras, quantum field theory, group actions, operator systems, and spectral triples.

  • C*-Algebras
  • Quantum Groups
  • Noncommutative Geometry
  • K-Theory
  • Locally Compact Groups
  • Von Neumann Algebras
  • Quantum Field Theory
  • Group Actions
  • Operator Systems
  • Spectral Triples
Research works
15k
fractional, since 1951
In the world top 10%
1.5k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+5%
the tick is no change
Largest producer
United States
26% of the 10 largest, 2022-now
Advanced Operator Algebra Research

Which countries lead Advanced Operator Algebra Research research?

By volume, the United States and China publish the most (360 and 234 works in 2022-now).

By volume, 2022-now

  1. 1 United States 360 works
  2. 2 China 234 works
  3. 3 Germany 123 works
  4. 4 India 117 works
  5. 5 France 115 works
  6. 6 Japan 104 works
  7. 7 Russia 93 works
  8. 8 United Kingdom 90 works
  9. 9 Italy 82 works
  10. 10 Iran 79 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 25.7%China: 16.7%Germany: 8.8%India: 8.4%6 others listed: 40.4%26%largest
United States360 · 25.7%China234 · 16.7%Germany123 · 8.8%India117 · 8.4%6 others listed564 · 40.4%

Shares of the rows listed above, not of the whole node.

Which institutions lead Advanced Operator Algebra Research research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Operator Algebra Research research, followed by Russian Academy of Sciences and Polish Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 59 works
  2. 2 Russian Academy of SciencesRussia 28 works
  3. 3 Polish Academy of SciencesPoland 13 works
  4. 4 KU LeuvenBelgium 13 works
  5. 5 East China Normal UniversityChina 13 works
  6. 6 University of MünsterGermany 13 works
  7. 7 The University of TokyoJapan 12 works
  8. 8 Indian Statistical InstituteIndia 12 works
  9. 9 Kyoto UniversityJapan 12 works
  10. 10 Lomonosov Moscow State UniversityRussia 12 works

Who are the leading researchers in Advanced Operator Algebra Research?

The most-cited researchers publishing on Advanced Operator Algebra Research include R. W. L. Jones and Edward H. Witten.

  1. 1 R. W. L. Jones United Kingdom 189k citations
  2. 2 Edward H. Witten United States 174k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

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).

Most cited papers
#PaperReleasedCitations
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 Open access 30 Sep 1999 3,743
3 Completely positive linear maps on complex matrices Man-Duen Choi · Linear Algebra and its Applications Open access 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
All 99 most cited papers, with filters and sorting

Where is Advanced Operator Algebra Research research done?

The largest centres of Advanced Operator Algebra Research research in 2022-now are Moscow (Russia), Shanghai (China), Paris (France) and Tokyo (Japan).

Largest cities, 2022-now

  1. 1 MoscowRussia 43 works
  2. 2 ShanghaiChina 37 works
  3. 3 ParisFrance 35 works
  4. 4 TokyoJapan 30 works
  5. 5 BeijingChina 30 works
  6. 6 TehranIran 20 works
  7. 7 WarsawPoland 19 works
  8. 8 PragueCzechia 18 works
  9. 9 KolkataIndia 18 works
  10. 10 RomeItaly 17 works
See Advanced Operator Algebra Research on the map

Where is the best place to study Advanced Operator Algebra Research?

Among universities, judged by research, University of Münster, University of Oxford and KU Leuven score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.

0%10%20%30%mean 14.53%fractional works in this field (log) →share of work in the world top 10% →University of OxfordUniversity of MünsterUNSW SydneyKU Leuven
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1University of MünsterGermany 86.223.5%15.8×12 +30.0%
2University of OxfordUnited Kingdom 81.325.3%4.1×11 +42.3%
3KU LeuvenBelgium 79.311.4%7.4×13 +56.3%
4UNSW SydneyAustralia 67.516.3%6.6×11 +10.2%
5University of ViennaAustria 60.814.9%10.1×9 +45.0%
6University of California San DiegoUnited States 55.511.3%5.6×10 +131.0%
7Kyoto UniversityJapan 55.211.9%8.2×12 -37.0%
8The University of TokyoJapan 54.911.2%5.3×12 -7.0%
9East China Normal UniversityChina 54.54.6%14.2×13 +63.4%
10University of GöttingenGermany 54.514.9%12.7×8 +23.6%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Advanced Operator Algebra Research, country by country

Is Advanced Operator Algebra Research research growing?

Output in 2022-2025 was 5% higher than in 2018-2021, peaking in 2016. The fastest-growing topics are Advanced Operator Algebra Research.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Advanced Operator Algebra Research as a percentage of every work published that year, 0.0083% in 2024.

still counting0.010%0.020%0.030%Advanced Operator Algebra Research0.0083% in 202519801990200020102020

Fractional works of Advanced Operator Algebra Research over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Advanced Operator Algebra Research10.0% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

Discussion

Ask a question or share a note about Advanced Operator Algebra Research. Posts are plain text and can be reported.