Victor Kac

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Victor Gershevich Kac
Born (1943-12-19) December 19, 1943 (age 74)
Buguruslan, Orenburg Oblast, Russia
Alma materMoscow State University (M.S.)
Moscow State University (Ph.D.)
Known for
Scientific career
ThesisSimple Irreducible Graded Lie Algebras of Finite Growth (1968)
Doctoral advisorÈrnest Borisovich Vinberg[1]

Victor Gershevich (Grigorievich) Kac (Russian: Виктор Гершевич (Григорьевич) Кац; born 19 December 1943 in Buguruslan, Russia, USSR) is a Soviet and American mathematician at MIT, known for his work in representation theory. He co-discovered[2] Kac–Moody algebras, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite-dimensional simple Lie superalgebras, and found the Kac determinant formula for the Virasoro algebra. He is also known for the Kac–Weisfeiler conjectures with Boris Weisfeiler.


Kac studied mathematics at Moscow State University, receiving his M.S. in 1965 and his Ph.D. in 1968.[3] From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Machine Building. He left the Soviet Union in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship in 1981 and a Guggenheim Fellowship in 1986 and the Medal of the College de France (1981). He received the Wigner Medal (1996) "in recognition of work on affine Lie algebras that has had wide influence in theoretical physics". In 1978 he was an Invited Speaker (Highest weight representations of infinite dimensional Lie algebras) at the ICM in Helsinki. Kac was a plenary speaker at the 1988 AMS centennial conference. In 2002 he gave a plenary lecture, Classification of Supersymmetries, at the ICM in Beijing.

Kac is a Fellow of the American Mathematical Society,[4] an Honorary member of the Moscow Mathematical Society, Fellow of the American Academy of Arts and Sciences and a Member of the National Academy of Sciences.

The research of Victor Kac primarily concerns representation theory and mathematical physics. His work appears in mathematics and physics and in the development of quantum field theory, string theory and the theory of integrable systems.

Kac-Moody algebra[edit]

"Almost simultaneously in 1967, Victor Kac in the USSR and Robert Moody in Canada developed what was to become Kac-Moody algebra. Kac and Moody noticed that if Wilhelm Killing's conditions were relaxed, it was still possible to associate to the Cartan matrix a Lie algebra which, necessarily, would be infinite dimensional." - A.J. Coleman[5]

Kac has published 13 books and over 200 articles in mathematics and physics journals and is listed as an ISI highly cited researcher.[6] Victor Kac was awarded the 2015 AMS Leroy P. Steele Prize for Lifetime Achievement.[7]

His brother Boris Katz is a principal research scientist at MIT.[8]


  • Kac, Victor G. (1994) [1985]. Infinite-Dimensional Lie Algebras (3rd ed.). Cambridge University Press. ISBN 0-521-46693-8.
  • Kac, Victor (1997). Vertex Algebras for Beginners (University Lecture Series, No 10). American Mathematical Society. ISBN 0-8218-0643-2.


  1. ^ Mathematics Genealogy Project:
  2. ^ Stephen Berman, Karen Parshall Victor Kac and Robert Moody — their paths to Kac–Moody-Algebras, Mathematical Intelligencer, 2002, Nr.1[1]
  3. ^ Victor Kac, A Biographical Interview:
  4. ^ List of Fellows of the American Mathematical Society, retrieved 2013-01-27.
  5. ^ Coleman, A. John, "The Greatest Mathematical Paper of All Time," The Mathematical Intelligencer, vol. 11, no. 3, pp. 29–38.
  6. ^ "List of ISI highly cited researchers".
  7. ^ 2015 AMS Steele Prizes
  8. ^ Negri, Gloria (4 October 2006). "Clara Katz; Soviet émigré saved ailing granddaughter". The Boston Globe.

External links[edit]