Victor Kac
Encyclopedia
Victor G. Kac is a Soviet and American
mathematician at MIT, known for his work in representation theory
. He discovered Kac–Moody algebra
s, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite dimensional simple Lie superalgebra
s, and found the Kac determinant formula for the Virasoro algebra
.
Kac studied mathematics at Moscow State University
, receiving his M.S. in 1965 and his Ph.D. in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Engineering
. 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.
His brother Boris Katz
is a principal research scientist at MIT.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician at MIT, known for his work in representation theory
Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studiesmodules over these abstract algebraic structures...
. He discovered Kac–Moody algebra
Kac–Moody algebra
In mathematics, a Kac–Moody algebra is a Lie algebra, usually infinite-dimensional, that can be defined by generators and relations through a generalized Cartan matrix...
s, and used the Weyl–Kac character formula for them to reprove the Macdonald identities. He classified the finite dimensional simple Lie superalgebra
Lie superalgebra
In mathematics, a Lie superalgebra is a generalisation of a Lie algebra to include a Z2-grading. Lie superalgebras are important in theoretical physics where they are used to describe the mathematics of supersymmetry...
s, and found the Kac determinant formula for the Virasoro algebra
Virasoro algebra
In mathematics, the Virasoro algebra is a complex Lie algebra, given as a central extension of the complex polynomial vector fields on the circle, and is widely used in conformal field theory and string theory....
.
Kac studied mathematics at Moscow State University
Moscow State University
Lomonosov Moscow State University , previously known as Lomonosov University or MSU , is the largest university in Russia. Founded in 1755, it also claims to be one of the oldest university in Russia and to have the tallest educational building in the world. Its current rector is Viktor Sadovnichiy...
, receiving his M.S. in 1965 and his Ph.D. in 1968. From 1968 to 1976, he held a teaching position at the Moscow Institute of Electronic Engineering
Moscow Institute of Electronic Engineering
Moscow Institute of Electronic EngineeringThere are two universities in Moscow, Russia, to which this name can refer.# In most cases this name refers to Moscow Institute of Electronic Technology, MIET and this was the official English name of the university early in the 1990s.# This name has been...
. He left the Soviet Union
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
in 1977, becoming an associate professor of mathematics at MIT. In 1981, he was promoted to full professor. Kac received a Sloan Fellowship
Sloan Fellowship
The Sloan Research Fellowships are awarded annually by the Alfred P. Sloan Foundation since 1955 to "provide support and recognition to early-career scientists and scholars". This is distinct from the Sloan Fellows in business....
in 1981 and a Guggenheim Fellowship
Guggenheim Fellowship
Guggenheim Fellowships are American grants that have been awarded annually since 1925 by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the arts." Each year, the foundation makes...
in 1986.
His brother Boris Katz
Boris Katz
Boris Katz is a Principal Research Scientist at the MIT Computer Science and Artificial Intelligence Laboratory and head of the Laboratory's InfoLab Group. His research interests include natural language processing and understanding, machine learning and intelligent information access...
is a principal research scientist at MIT.