H-Index & Metrics Top Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics H-index 75 Citations 30,532 249 World Ranking 78 National Ranking 45

Research.com Recognitions

Awards & Achievements

2015 - Steele Prize for Lifetime Achievement

2013 - Fellow of the American Mathematical Society

2013 - Member of the National Academy of Sciences

2007 - Fellow of the American Academy of Arts and Sciences

1986 - Fellow of John Simon Guggenheim Memorial Foundation

1981 - Fellow of Alfred P. Sloan Foundation

Overview

What is he best known for?

The fields of study he is best known for:

  • Algebra
  • Pure mathematics
  • Vector space

The scientist’s investigation covers issues in Pure mathematics, Algebra, Lie conformal algebra, Representation of a Lie group and Affine Lie algebra. His study connects Discrete mathematics and Pure mathematics. His Algebra research is multidisciplinary, incorporating perspectives in Current algebra, Algebra representation, Algebra over a field, Generalization and Vertex operator algebra.

The various areas that Victor G. Kac examines in his Lie conformal algebra study include Korteweg–de Vries equation and Linear independence. His biological study spans a wide range of topics, including Killing form, Adjoint representation of a Lie algebra, -module, Graded Lie algebra and Simple Lie group. His study explores the link between Kac–Moody algebra and topics such as Cartan matrix that cross with problems in Verma module, Affine root system, Generalized Verma module and Loop algebra.

His most cited work include:

  • Infinite-Dimensional Lie Algebras (4874 citations)
  • Vertex algebras for beginners (951 citations)
  • Basic representations of affine Lie algebras and dual resonance models (715 citations)

What are the main themes of his work throughout his whole career to date?

Victor G. Kac mainly focuses on Pure mathematics, Algebra, Lie conformal algebra, Lie algebra and Affine Lie algebra. His Pure mathematics study combines topics from a wide range of disciplines, such as Conformal map and Simple. The Algebra study combines topics in areas such as Primary field, Conformal field theory and Algebra representation.

His studies in Lie conformal algebra integrate themes in fields like Current algebra, Universal enveloping algebra and Graded Lie algebra. As part of one scientific family, he deals mainly with the area of Graded Lie algebra, narrowing it down to issues related to the Simple Lie group, and often Discrete mathematics. His work deals with themes such as Representation of a Lie group, Verma module and Adjoint representation of a Lie algebra, which intersect with Affine Lie algebra.

He most often published in these fields:

  • Pure mathematics (58.46%)
  • Algebra (30.26%)
  • Lie conformal algebra (19.74%)

What were the highlights of his more recent work (between 2016-2021)?

  • Pure mathematics (58.46%)
  • Lie algebra (18.97%)
  • Vertex (10.77%)

In recent papers he was focusing on the following fields of study:

Victor G. Kac focuses on Pure mathematics, Lie algebra, Vertex, Vertex operator algebra and Combinatorics. He combines subjects such as Quantum and Type with his study of Pure mathematics. Victor G. Kac interconnects Affine Lie algebra, Yangian, Simple, Element and Nilpotent in the investigation of issues within Lie algebra.

His Affine Lie algebra research incorporates elements of Ramanujan theta function, Superconformal algebra, Lie conformal algebra, Modular invariance and Invariant. His work carried out in the field of Verma module brings together such families of science as Representation of a Lie group and Generalized Verma module. Victor G. Kac has included themes like Korteweg–de Vries equation and Algebra in his Hamiltonian system study.

Between 2016 and 2021, his most popular works were:

  • Conformal embeddings of affine vertex algebras in minimal W-algebras I: Structural results (36 citations)
  • A remark on boundary level admissible representations (29 citations)
  • Conformal embeddings of affine vertex algebras in minimal W-algebras II: decompositions (20 citations)

In his most recent research, the most cited papers focused on:

  • Algebra
  • Pure mathematics
  • Vector space

His scientific interests lie mostly in Pure mathematics, Vertex operator algebra, Lie algebra, Vertex and Combinatorics. Many of his studies involve connections with topics such as Wave function and Pure mathematics. His Lie algebra study incorporates themes from Discrete mathematics, Affine representation and Affine transformation.

His biological study deals with issues like Affine Lie algebra, which deal with fields such as Quantum affine algebra. The concepts of his Integrable system study are interwoven with issues in Hamiltonian and Lie conformal algebra. His Hamiltonian system research integrates issues from Korteweg–de Vries equation and 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.

Top Publications

Infinite-Dimensional Lie Algebras

Victor G. Kac.
idla (1990)

7357 Citations

Vertex algebras for beginners

Victor G. Kac.
(1997)

1276 Citations

Basic representations of affine Lie algebras and dual resonance models

I.B. Frenkel;V.G. Kac.
Inventiones Mathematicae (1980)

1019 Citations

Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras

Victor G. Kac;A. K. Raina.
(1983)

930 Citations

Infinite-dimensional Lie algebras, theta functions and modular forms

Victor G Kač;Dale H Peterson.
Advances in Mathematics (1984)

886 Citations

Representations of classical lie superalgebras

V. Kac.
(1978)

644 Citations

A sketch of Lie superalgebra theory

V. G. Kac.
Communications in Mathematical Physics (1977)

594 Citations

SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH

V G Kac.
Mathematics of The Ussr-izvestiya (1968)

551 Citations

Infinite root systems, representations of graphs and invariant theory

V. G. Kac.
Inventiones Mathematicae (1980)

515 Citations

Structure of representations with highest weight of infinite-dimensional Lie algebras☆

V.G Kac;D.A Kazhdan.
Advances in Mathematics (1979)

439 Citations

Profile was last updated on December 6th, 2021.
Research.com Ranking is based on data retrieved from the Microsoft Academic Graph (MAG).
The ranking h-index is inferred from publications deemed to belong to the considered discipline.

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