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
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.
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, 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.
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.
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Vertex operator algebras and the Monster
Igor Frenkel;James Lepowsky;Arne Meurman.
Pure and Applied Mathematics (1988)
Basic representations of affine Lie algebras and dual resonance models
I.B. Frenkel;V.G. Kac.
Inventiones Mathematicae (1980)
On Axiomatic Approaches to Vertex Operator Algebras and Modules
Igor B. Frenkel;Yi-Zhi Huang;James Lepowsky.
Vertex operator algebras associated to representations of affine and Virasoro Algebras
Igor B. Frenkel;Yongchang Zhu.
Duke Mathematical Journal (1992)
Quantum affine algebras and holonomic difference equations
I. B. Frenkel;N. Yu. Reshetikhin.
Communications in Mathematical Physics (1992)
Four‐dimensional topological quantum field theory, Hopf categories, and the canonical bases
Louis Crane;Igor B. Frenkel.
Journal of Mathematical Physics (1994)
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)
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)
Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
Pavel Etingof;Igor Frenkel;Alexander Kirillov.
Spinor Construction of Vertex Operator Algebras, Triality, and E
Alex J. Feingold;Igor B. Frenkel;John F. X. Ries.
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