Igor Frenkel

6.9k total citations · 3 hit papers
53 papers, 3.5k citations indexed

About

Igor Frenkel is a scholar working on Geometry and Topology, Algebra and Number Theory and Mathematical Physics. According to data from OpenAlex, Igor Frenkel has authored 53 papers receiving a total of 3.5k indexed citations (citations by other indexed papers that have themselves been cited), including 45 papers in Geometry and Topology, 35 papers in Algebra and Number Theory and 23 papers in Mathematical Physics. Recurrent topics in Igor Frenkel's work include Algebraic structures and combinatorial models (43 papers), Advanced Topics in Algebra (34 papers) and Nonlinear Waves and Solitons (19 papers). Igor Frenkel is often cited by papers focused on Algebraic structures and combinatorial models (43 papers), Advanced Topics in Algebra (34 papers) and Nonlinear Waves and Solitons (19 papers). Igor Frenkel collaborates with scholars based in United States, Germany and United Kingdom. Igor Frenkel's co-authors include Victor G. Kač, Yongchang Zhu, James Lepowsky, Yi-Zhi Huang, Nicolai Reshetikhin, Alex J. Feingold, Mikhail Khovanov, Naihuan Jing, Pavel Etingof and Arne Meurman and has published in prestigious journals such as Proceedings of the National Academy of Sciences, Communications in Mathematical Physics and Inventiones mathematicae.

In The Last Decade

Igor Frenkel

51 papers receiving 3.2k citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Basic representations of affine Lie algebras and dual resonance models

1980 495 citations Igor Frenkel et al. profile →
On axiomatic approaches to vertex operator algebras and modules

1993 481 citations Igor Frenkel et al. profile →
Vertex operator algebras associated to representations of affine and Virasoro algebras

1992 442 citations Igor Frenkel et al. profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Igor Frenkel United States	24	3.1k	2.2k	1.9k	1.1k	596	53	3.5k
Boris Feigin Russia	32	2.6k 0.8×	1.6k 0.7×	1.4k 0.7×	989 0.9×	851 1.4×	134	2.9k
James Lepowsky United States	28	3.6k 1.2×	2.9k 1.4×	1.8k 1.0×	1.5k 1.3×	470 0.8×	69	4.1k
Christian Kassel France	17	3.2k 1.0×	2.5k 1.2×	1.3k 0.7×	1.8k 1.7×	274 0.5×	38	3.8k
Pavel Etingof United States	35	3.8k 1.3×	2.6k 1.2×	1.5k 0.8×	2.3k 2.1×	262 0.4×	193	4.4k
Giovanni Felder Switzerland	26	1.5k 0.5×	776 0.4×	1.2k 0.6×	988 0.9×	965 1.6×	90	2.4k
Maxim Kontsevich France	20	2.3k 0.8×	1.2k 0.5×	1.0k 0.6×	2.1k 1.9×	813 1.4×	44	3.3k
Shahn Majid United Kingdom	31	3.0k 1.0×	2.3k 1.0×	2.3k 1.2×	1.7k 1.6×	1.3k 2.1×	146	4.2k
Vladimir G. Turaev Russia	18	2.6k 0.8×	547 0.3×	535 0.3×	2.0k 1.8×	508 0.9×	36	3.1k
E. K. Sklyanin Russia	18	2.8k 0.9×	1.2k 0.5×	2.3k 1.2×	473 0.4×	726 1.2×	35	3.6k
M. Scheunert Germany	20	1.3k 0.4×	1.2k 0.5×	985 0.5×	433 0.4×	348 0.6×	36	1.9k

Countries citing papers authored by Igor Frenkel

Since Specialization

Citations

This map shows the geographic impact of Igor Frenkel's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Igor Frenkel with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Igor Frenkel more than expected).

Fields of papers citing papers by Igor Frenkel

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Igor Frenkel. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Igor Frenkel. The network helps show where Igor Frenkel may publish in the future.

Co-authorship network of co-authors of Igor Frenkel

This figure shows the co-authorship network connecting the top 25 collaborators of Igor Frenkel. A scholar is included among the top collaborators of Igor Frenkel based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Igor Frenkel. Igor Frenkel is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

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20 of 20 papers shown

1.

Frenkel, Igor & Robert Penner. (2022). Sketch of a Program for Automorphic Functions from Universal Teichmüller Theory to Capture Monstrous Moonshine. Communications in Mathematical Physics. 389(3). 1525–1567. 2 indexed citations

2.

Frenkel, Igor & Anton M. Zeitlin. (2013). Quantum group $\mathrm{GL}_q(2)$ and quantum Laplace operator via semi-infinite cohomology. Journal of Noncommutative Geometry. 7(4). 1007–1026. 1 indexed citations

3.

Frenkel, Igor, et al.. (2012). Vertex algebras associated to modified regular representations of the Virasoro algebra. Advances in Mathematics. 229(6). 3468–3507. 6 indexed citations

4.

Frenkel, Igor, et al.. (2011). Split quaternionic analysis and separation of the series for SL(2,R) and SL(2,C)/SL(2,R). Advances in Mathematics. 228(2). 678–763. 21 indexed citations

5.

Frenkel, Igor, et al.. (2008). Quaternionic analysis, representation theory and physics. Advances in Mathematics. 218(6). 1806–1877. 38 indexed citations

6.

Frenkel, Igor & Marcos Jardim. (2008). Complex ADHM equations and sheaves on P3. Journal of Algebra. 319(7). 2913–2937. 12 indexed citations

7.

Frenkel, Igor & Andrey Todorov. (2007). Complex counterpart of Chern-Simons-Witten theory and holomorphic linking. Advances in Theoretical and Mathematical Physics. 11(4). 531–590. 5 indexed citations

8.

Frenkel, Igor, et al.. (2005). Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology. Advances in Mathematics. 206(1). 57–111. 10 indexed citations

9.

Frenkel, Igor & Weiqiang Wang. (2001). Virasoro Algebra and Wreath Product Convolution. Journal of Algebra. 242(2). 656–671. 17 indexed citations

10.

Bernstein, Joseph, Igor Frenkel, & Mikhail Khovanov. (2000). A Categorification of the Temperley-Lieb Algebra and Schur Quotients of U(sl2) via Projective and. arXiv (Cornell University). 2 indexed citations

11.

Bernstein, Joseph, Igor Frenkel, & Mikhail Khovanov. (1999). A categorification of the Temperley-Lieb algebra and Schur quotients of $ U({\frak sl}_2) $ via projective and Zuckerman functors. Selecta Mathematica. 5(2). 199–241. 74 indexed citations

12.

Etingof, Pavel, Igor Frenkel, & Alexander Kirillov. (1998). Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations. Mathematical surveys and monographs. 134 indexed citations

13.

Frenkel, Igor, Alexander Kirillov, & Alexander Varchenko. (1997). . International Mathematics Research Notices. 1997(16). 783–783. 2 indexed citations

14.

Feingold, Alex J., et al.. (1993). Representations of Hyperbolic Kac-Moody Algebras. Journal of Algebra. 156(2). 433–453. 6 indexed citations

15.

Feingold, Alex J., et al.. (1991). Spinor Construction of Vertex Operator Algebras, Triality, and 𝐸⁽¹⁾₈. Contemporary mathematics - American Mathematical Society. 23 indexed citations

16.

Frenkel, Igor & Gregory Moore. (1991). Simplex equations and their solutions. Communications in Mathematical Physics. 138(2). 259–271. 21 indexed citations

17.

Frenkel, Igor, et al.. (1987). VERTEX OPERATOR CALCULUS. 150–188. 105 indexed citations

18.

Frenkel, Igor, Howard Garland, & Gregg J. Zuckerman. (1986). Semi-infinite cohomology and string theory. Proceedings of the National Academy of Sciences. 83(22). 8442–8446. 95 indexed citations

19.

Feingold, Alex J. & Igor Frenkel. (1985). Classical affine algebras. Advances in Mathematics. 56(2). 117–172. 64 indexed citations

20.

Frenkel, Igor. (1981). Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory. Journal of Functional Analysis. 44(3). 259–327. 126 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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