- Home
- Best Scientists - Mathematics
- Igor B. Frenkel

Discipline name
D-index
D-index (Discipline H-index) only includes papers and citation values for an examined
discipline in contrast to General H-index which accounts for publications across all
disciplines.
Citations
Publications
World Ranking
National Ranking

Mathematics
D-index
33
Citations
11,923
96
World Ranking
2109
National Ranking
900

2018 - Member of the National Academy of Sciences

2015 - Fellow of the American Academy of Arts and Sciences

1990 - Fellow of John Simon Guggenheim Memorial Foundation

1984 - Fellow of Alfred P. Sloan Foundation

- Algebra
- Pure mathematics
- Quantum mechanics

His primary scientific interests are in Algebra, Pure mathematics, Quantum affine algebra, Affine Lie algebra and Lie conformal algebra. His work deals with themes such as Calculus and Calculus, which intersect with Algebra. His Quantum affine algebra research includes elements of Quantum algebra, Quantum algorithm and Quantum group.

In his work, Operator algebra and Discrete mathematics is strongly intertwined with Lie algebra, which is a subfield of Quantum algebra. His research brings together the fields of Vertex operator algebra and Lie conformal algebra. He combines Nest algebra and Knizhnik–Zamolodchikov equations in his research.

- Vertex Operator Algebras and the Monster (1743 citations)
- On Axiomatic Approaches to Vertex Operator Algebras and Modules (959 citations)
- Basic representations of affine Lie algebras and dual resonance models (715 citations)

His scientific interests lie mostly in Pure mathematics, Algebra, Representation theory, Lie algebra and Affine transformation. His research in Pure mathematics tackles topics such as Group which are related to areas like Classification theorem, Complex Lie group, Umbral moonshine and Conjugacy class. His Representation theory research is multidisciplinary, incorporating elements of Minkowski space, Complete intersection and Euler's formula.

His Affine transformation research is multidisciplinary, relying on both Simple, Fock space and Finite group. The concepts of his Affine Lie algebra study are interwoven with issues in Representation theory of SU and Lie conformal algebra. His study in Lie conformal algebra is interdisciplinary in nature, drawing from both Discrete mathematics, Universal enveloping algebra and Vertex operator algebra.

- Pure mathematics (62.71%)
- Algebra (27.97%)
- Representation theory (17.80%)

- Pure mathematics (62.71%)
- Representation theory (17.80%)
- Quaternionic analysis (7.63%)

Pure mathematics, Representation theory, Quaternionic analysis, Lie algebra and Conformal group are his primary areas of study. The various areas that Igor Frenkel examines in his Pure mathematics study include Group and Algebra. His studies in Algebra integrate themes in fields like Current algebra, Virasoro algebra, Algebra representation and Vertex operator algebra.

His Representation theory study which covers Categorification that intersects with Order, Functor, Euler's formula and Simple. In his study, Laurent series, Basis function, Holomorphic function and Modular group is inextricably linked to Invariant, which falls within the broad field of Lie algebra. His Monster Lie algebra study integrates concerns from other disciplines, such as Umbral moonshine, Operator theory, Verma module and Knizhnik–Zamolodchikov equations.

- Vertex Operator Algebras and the Monster (1743 citations)
- Rademacher sums, moonshine and gravity (71 citations)
- Categorifying fractional Euler characteristics, Jones–Wenzl projectors and 3j-symbols (51 citations)

- Pure mathematics
- Algebra
- Quantum mechanics

His primary areas of investigation include Pure mathematics, Representation theory, Lie algebra, Monstrous moonshine and Quaternionic analysis. His study in the field of Euler characteristic, Unipotent and Tensor product is also linked to topics like Mellin transform. He has researched Representation theory in several fields, including Simple, Quantum group, Categorification and Euler's formula.

His research integrates issues of Differential operator, Invariant and Feynman diagram in his study of Lie algebra. He interconnects Combinatorics, Modular group, Umbral moonshine, Verma module and Monster Lie algebra in the investigation of issues within Monstrous moonshine. His Monster Lie algebra research integrates issues from Knizhnik–Zamolodchikov equations, Operator theory and Lie conformal algebra.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Vertex operator algebras and the Monster

Igor Frenkel;James Lepowsky;Arne Meurman.

Pure and Applied Mathematics **(1988)**

2830 Citations

Basic representations of affine Lie algebras and dual resonance models

I.B. Frenkel;V.G. Kac.

Inventiones Mathematicae **(1980)**

1066 Citations

On Axiomatic Approaches to Vertex Operator Algebras and Modules

Igor B. Frenkel;Yi-Zhi Huang;James Lepowsky.

**(1993)**

1045 Citations

Vertex operator algebras associated to representations of affine and Virasoro Algebras

Igor B. Frenkel;Yongchang Zhu.

Duke Mathematical Journal **(1992)**

865 Citations

Quantum affine algebras and holonomic difference equations

I. B. Frenkel;N. Yu. Reshetikhin.

Communications in Mathematical Physics **(1992)**

703 Citations

Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases

Louis Crane;Igor B. Frenkel.

Journal of Mathematical Physics **(1994)**

363 Citations

Vertex representations of quantum affine algebras.

Igor B. Frenkel;Naihuan Jing.

Proceedings of the National Academy of Sciences of the United States of America **(1988)**

348 Citations

A natural representation of the Fischer-Griess Monster with the modular function J as character

Igor Frenkel;James Lepowsky;Arne Meurman.

Proceedings of the National Academy of Sciences of the United States of America **(1984)**

329 Citations

Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations

Pavel Etingof;Igor Frenkel;Alexander Kirillov.

**(1998)**

313 Citations

Spinor Construction of Vertex Operator Algebras, Triality, and E

Alex J. Feingold;Igor B. Frenkel;John F. X. Ries.

**(1991)**

305 Citations

If you think any of the details on this page are incorrect, let us know.

Contact us

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Rutgers, The State University of New Jersey

Columbia University

University of Virginia

MIT

National Research University Higher School of Economics

University of North Carolina at Chapel Hill

Indiana University

Rutgers, The State University of New Jersey

MIT

Rutgers, The State University of New Jersey

Aristotle University of Thessaloniki

University of Southampton

Nitek (United States)

Nanyang Technological University

University of Colorado Boulder

Osaka University

Qatar University

Zhejiang University

Georgetown University Medical Center

University of Massachusetts Medical School

University of California, Davis

Mount Allison University

University of Sussex

University of Tübingen

University of California, Los Angeles

University of Pennsylvania

Something went wrong. Please try again later.