Lajos Pukánszky
Encyclopedia
Lajos Pukánszky was a Hungarian and American mathematician noted for his work in representation theory
of solvable
Lie group
s. He was born in Budapest
on November 24, 1928, defended his thesis in 1955 at the University of Szeged
under Béla Szőkefalvi-Nagy
, but left Hungary in 1956. After taking several posts in the United States (at the Research Institute of Advanced Studies in Baltimore, the University of Maryland, College Park
, Stanford University
, UCLA), in 1965 he became a professor at the University of Pennsylvania
, where he stayed until his retirement. He gave an invited address at the International Congress of Mathematicians
in Nice in 1970. In 1988 a conference entitled "The Orbit Method in Representation Theory" was held at the University of Copenhagen
in honor of his sixtieth birthday. He died on February 15, 1996, in Philadelphia.
s and related subjects. In 1956 he constructed two nonisomorphic factors of type III. A bulk of his later work was devoted to the unitary representation theory of solvable
Lie group
s. He found a geometric condition, known as the Pukánszky condition, that allowed an extension of the orbit method
from nilpotent to solvable Lie groups and played a major role in the subsequent development of the theory. Later he considered unitary representations of general separable locally compact groups and, in particular, gave a characterization for their being CCR groups or type I groups.
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...
of solvable
Solvable group
In mathematics, more specifically in the field of group theory, a solvable group is a group that can be constructed from abelian groups using extensions...
Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s. He was born in Budapest
Budapest
Budapest is the capital of Hungary. As the largest city of Hungary, it is the country's principal political, cultural, commercial, industrial, and transportation centre. In 2011, Budapest had 1,733,685 inhabitants, down from its 1989 peak of 2,113,645 due to suburbanization. The Budapest Commuter...
on November 24, 1928, defended his thesis in 1955 at the University of Szeged
University of Szeged
The University of Szeged is one of Hungary's most distinguished universities, and is among the most prominent higher education institutions in Central Europe...
under Béla Szőkefalvi-Nagy
Bela Szokefalvi-Nagy
Béla Szőkefalvi-Nagy was a Hungarian mathematician. His father, Gyula Szőkefalvi-Nagy was also a famed mathematician. Szőkefalvi-Nagy collaborated with Alfréd Haar and Frigyes Riesz, founders of the Szegedian school of mathematics. He contributed to the theory of Fourier series and approximation...
, but left Hungary in 1956. After taking several posts in the United States (at the Research Institute of Advanced Studies in Baltimore, the University of Maryland, College Park
University of Maryland, College Park
The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...
, Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
, UCLA), in 1965 he became a professor at the University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...
, where he stayed until his retirement. He gave an invited address at the International Congress of Mathematicians
International Congress of Mathematicians
The International Congress of Mathematicians is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union ....
in Nice in 1970. In 1988 a conference entitled "The Orbit Method in Representation Theory" was held at the University of Copenhagen
University of Copenhagen
The University of Copenhagen is the oldest and largest university and research institution in Denmark. Founded in 1479, it has more than 37,000 students, the majority of whom are female , and more than 7,000 employees. The university has several campuses located in and around Copenhagen, with the...
in honor of his sixtieth birthday. He died on February 15, 1996, in Philadelphia.
Scientific work
Pukánszky's early work concerned von Neumann algebraVon Neumann algebra
In mathematics, a von Neumann algebra or W*-algebra is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology and contains the identity operator. They were originally introduced by John von Neumann, motivated by his study of single operators, group...
s and related subjects. In 1956 he constructed two nonisomorphic factors of type III. A bulk of his later work was devoted to the unitary representation theory of solvable
Solvable group
In mathematics, more specifically in the field of group theory, a solvable group is a group that can be constructed from abelian groups using extensions...
Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s. He found a geometric condition, known as the Pukánszky condition, that allowed an extension of the orbit method
Kirillov orbit theory
In mathematics, the orbit method establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits: orbits of the action of the group on the dual space of its Lie algebra...
from nilpotent to solvable Lie groups and played a major role in the subsequent development of the theory. Later he considered unitary representations of general separable locally compact groups and, in particular, gave a characterization for their being CCR groups or type I groups.
Selected papers
- Unitary representations of solvable Lie groups, Ann. Sci. École Norm. Sup. 4 (1971), 457–608
- Characters of connected Lie groups, Acta Math.Acta MathematicaActa Mathematica is a journal publishing original research papers in all fields of mathematics. The journal was founded by Gösta Mittag-Leffler in 1882 and is published by Institut Mittag-Leffler, a research institute for mathematics belonging to the Royal Swedish Academy of Sciences...
133 (1974), 81–137