Advanced Topics in Algebra

Advanced Topics in Algebra is a research topic within Algebra and Number Theory. Science Explorer counts 46k research works in it since 1950. 9.8% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the deformations, structures, and classifications of Hom-Lie algebras, including their connections to Hopf algebras, renormalization in quantum field theory, derivations, and cohomology. It also explores related topics such as Baxter algebras, quasi-Lie algebras, and gradings.

Hom-Lie Algebras
Deformations
Hopf Algebra
Renormalization
Derivations
Baxter Algebras
Quasi-Lie Algebras
Homology
Gradings
Cohomology

Research works: 46k
In the world top 10%: 4.6k
Top-10% rate: 9.8%
Growth, 2018-21 → 2022-25: +14%
Largest producer: China

Advanced Topics in Algebra

Which countries lead Advanced Topics in Algebra research?

By volume, China and the United States publish the most (916 and 655 works in 2022-now).

By volume, 2022-now

1 China 916 works
2 United States 655 works
3 India 406 works
4 Russia 285 works
5 France 241 works
6 Germany 231 works
7 Japan 209 works
8 Iran 204 works
9 United Kingdom 187 works
10 Italy 173 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.

China916 · 26.1%United States655 · 18.7%India406 · 11.6%Russia285 · 8.1%6 others listed1,245 · 35.5%

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

Which institutions lead Advanced Topics in Algebra research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Advanced Topics in Algebra research, followed by Russian Academy of Sciences and Aligarh Muslim University.

By volume, 2022-now

1 Centre National de la Recherche ScientifiqueFrance 119 works
2 Russian Academy of SciencesRussia 67 works
3 Aligarh Muslim UniversityIndia 46 works
4 Sidi Mohamed Ben Abdellah UniversityMorocco 36 works
5 Lomonosov Moscow State UniversityRussia 34 works
6 University of SfaxTunisia 30 works
7 Universidade de São PauloBrazil 25 works
8 The University of TokyoJapan 25 works
9 National Research University Higher School of EconomicsRussia 23 works
10 National Academy of Sciences of UkraineUkraine 23 works

Who are the leading researchers in Advanced Topics in Algebra?

The most-cited researchers publishing on Advanced Topics in Algebra include Kieron Burke, John C. Morris and Stephen M. Smith.

1 Kieron Burke United States 276k citations
2 John C. Morris United States 241k citations
3 Stephen M. Smith United Kingdom 214k citations
4 Edward H. Witten United States 174k citations
5 B. S. Acharya France 164k 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 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).

Most cited papers
#	Paper	Released	Citations
1	The Magma Algebra System I: The User Language Wieb Bosma, John Cannon, Catherine Playoust · Journal of Symbolic Computation Open access	Sep 1997	7,465
2	Completely positive linear maps on complex matrices Man-Duen Choi · Linear Algebra and its Applications Open access	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 Conference paper	28 Oct 1993	2,592
5	Deformation Quantization of Poisson Manifolds Maxim L'vovich Kontsevich · Letters in Mathematical Physics Open access	Dec 2003	2,463

All 100 most cited papers, with filters and sorting

Where is Advanced Topics in Algebra research done?

The largest centres of Advanced Topics in Algebra research in 2022-now are Moscow (Russia), Shanghai (China), Beijing (China) and Paris (France). Among places with at least 20 works in it, it is an unusually large share of all research in Aligarh, Fes and Sfax.

Largest cities, 2022-now

1 MoscowRussia 149 works
2 ShanghaiChina 91 works
3 BeijingChina 89 works
4 ParisFrance 76 works
5 TokyoJapan 66 works
6 TehranIran 56 works
7 NanjingChina 53 works
8 AligarhIndia 46 works
9 PragueCzechia 42 works
10 ChangchunChina 39 works

Where it is the local speciality

AligarhIN · 46.3 works27×
FesMA · 36.1 works18×
SfaxTN · 30.4 works15×

← less than its size predicts1×more →

Location quotient: how much more of its research is in Advanced Topics in Algebra than the world average.

See Advanced Topics in Algebra on the map

Where is the best place to study Advanced Topics in Algebra?

Among universities, judged by research, Massachusetts Institute of Technology, University of Edinburgh and Aligarh Muslim University 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.

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.

#	University	Score	Top 10%	Specialisation	Works	Growth
1	Massachusetts Institute of TechnologyUnited States	76.2	16.0%	5.5×	19	+45.7%
2	University of EdinburghUnited Kingdom	73.1	24.9%	3.6×	15	+38.2%
3	Aligarh Muslim UniversityIndia	71.9	12.6%	31.8×	46	+85.3%
4	The University of TokyoJapan	71.0	20.3%	4.0×	24	+22.8%
5	University of OxfordUnited Kingdom	69.3	22.2%	2.3×	16	+42.2%
6	University of BonnGermany	69.0	25.1%	5.1×	12	+70.0%
7	Jilin UniversityChina	68.2	23.5%	3.2×	18	+81.3%
8	University of PalermoItaly	68.2	23.7%	8.0×	13	+20.9%
9	New York UniversityUnited States	66.4	21.8%	2.4×	13	+208.7%
10	University of SfaxTunisia	65.5	8.0%	25.1×	30	+86.6%
11	Kyoto UniversityJapan	64.8	16.2%	5.2×	19	+8.0%
12	Université Paris-SaclayFrance	61.2	19.9%	3.0×	10	+91.5%
13	Tsinghua UniversityChina	60.9	13.8%	1.9×	21	+60.3%
14	Nankai UniversityChina	59.9	21.7%	4.7×	16	+84.8%
15	Mälardalen UniversitySweden	59.5	14.5%	32.3×	8	+99.6%
16	Lomonosov Moscow State UniversityRussia	58.7	8.5%	8.2×	34	-5.8%
17	National Research University Higher School of EconomicsRussia	58.5	10.5%	11.7×	23	+15.8%
18	KU LeuvenBelgium	58.2	10.6%	3.0×	14	+122.1%
19	University of CopenhagenDenmark	56.8	13.0%	2.6×	12	+90.3%
20	Indian Institute of Technology KharagpurIndia	56.8	19.6%	4.7×	11	+633.5%
21	Universitat Autònoma de BarcelonaSpain	54.6	24.9%	3.0×	10	-7.1%
22	Sidi Mohamed Ben Abdellah UniversityMorocco	54.1	2.5%	27.2×	36	+78.0%
23	Shanghai UniversityChina	54.0	17.2%	3.5×	12	+26.6%
24	University of NisSerbia	53.6	16.2%	13.8×	11	-21.2%
25	University of MünsterGermany	53.3	17.7%	5.9×	12	+10.5%
26	University of Rome Tor VergataItaly	52.7	15.3%	7.2×	11	+80.5%
27	Charles UniversityCzechia	52.1	12.4%	5.7×	13	+77.2%
28	The University of SydneyAustralia	51.8	28.3%	1.5×	9	-20.6%
29	University of VirginiaUnited States	51.4	16.4%	3.2×	10	+38.2%
30	University of WarsawPoland	51.3	23.8%	3.4×	8	+24.1%
31	University of TorontoCanada	50.8	15.4%	1.2×	12	+155.4%
32	Aarhus UniversityDenmark	50.6	10.6%	2.5×	11	+262.5%
33	University of Science and Technology of ChinaChina	50.5	12.9%	2.4×	14	+70.1%
34	Rutgers, The State University of New JerseyUnited States	50.3	19.9%	2.7×	10	-14.1%
35	Utrecht UniversityNetherlands	49.9	6.1%	2.7×	9	+212.2%
36	Uppsala UniversitySweden	49.2	6.5%	4.3×	11	+63.0%
37	Indian Statistical InstituteIndia	48.7	10.3%	31.4×	13	+33.3%
38	National University of UzbekistanUzbekistan	48.5	13.4%	15.9×	12	-3.1%
39	Vrije Universiteit BrusselBelgium	48.5	17.4%	6.0×	8	-14.3%
40	East China Normal UniversityChina	48.4	5.9%	7.0×	16	+30.0%
41	Capital Normal UniversityChina	48.4	16.0%	12.4×	8	+23.3%
42	Northeast Normal UniversityChina	48.1	9.3%	15.6×	16	+36.9%
43	University of California, BerkeleyUnited States	47.3	18.7%	1.8×	8	-9.7%
44	University of MonastirTunisia	45.7	6.1%	13.7×	10	+116.7%
45	University of OsloNorway	44.8	4.9%	2.8×	9	+158.0%
46	Universidade de São PauloBrazil	44.6	4.2%	2.5×	25	+6.3%
47	University of GafsaTunisia	44.1	6.9%	93.0×	9	+232.7%
48	King Abdulaziz UniversitySaudi Arabia	42.7	11.1%	4.0×	10	-6.9%
49	Ghent UniversityBelgium	39.7	8.0%	2.4×	9	+17.3%
50	Islamic Azad University, TehranIran	28.2	0.8%	2.8×	23	-50.0%

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 Topics in Algebra, country by country

Is Advanced Topics in Algebra research growing?

Output in 2022-2025 was 14% higher than in 2018-2021, peaking in 2024. The fastest-growing topics are Advanced Topics in Algebra.

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 Topics in Algebra as a percentage of every work published that year, 0.027% in 2024.

Fractional works of Advanced Topics in Algebra 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.

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

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Which countries lead Advanced Topics in Algebra research?

By volume, 2022-now

How concentrated that is

Which institutions lead Advanced Topics in Algebra research?

By volume, 2022-now

Who are the leading researchers in Advanced Topics in Algebra?

What are the most cited papers in Advanced Topics in Algebra?

Where is Advanced Topics in Algebra research done?

Largest cities, 2022-now

Where it is the local speciality

Where is the best place to study Advanced Topics in Algebra?

Is Advanced Topics in Algebra research growing?

Its share of all research

How much of it reaches the world top 10%

Which topics inside it are moving

Related research

Discussion