Lajos Pukánszky (1928-1996) was a Hungarian and American mathematician noted for his work in

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

of solvable

Lie group In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Eucli ...

s. He was born in

Budapest Budapest is the Capital city, capital and List of cities and towns of Hungary, most populous city of Hungary. It is the List of cities in the European Union by population within city limits, tenth-largest city in the European Union by popul ...

on November 24, 1928, defended his thesis in 1955 at the

University of Szeged The University of Szeged () is a Public university, public research university in Szeged, Hungary. Established as the Jesuit Academy of Kolozsvár in present-day Cluj-Napoca in 1581, the institution was re-established as a university in 1872 by ...

under

Béla Szőkefalvi-Nagy Béla Szőkefalvi-Nagy (29 July 1913, Kolozsvár – 21 December 1998, Szeged) was a Hungarian mathematician. His father, Gyula Szőkefalvi-Nagy was also a famed mathematician. Szőkefalvi-Nagy collaborated with Alfréd Haar and Frigyes Riesz ...

, 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 The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD i ...

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California, United States. Its academic roots were established in 1881 as a normal school then known as the southern branch of the C ...

), in 1965 he became a professor at the

University of Pennsylvania The University of Pennsylvania (Penn or UPenn) is a Private university, private Ivy League research university in Philadelphia, Pennsylvania, United States. One of nine colonial colleges, it was chartered in 1755 through the efforts of f ...

, 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 The University of Copenhagen (, KU) is a public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in Scandinavia, after Uppsala University. ...

in honor of his sixtieth birthday. He died on February 15, 1996, in

Philadelphia Philadelphia ( ), colloquially referred to as Philly, is the List of municipalities in Pennsylvania, most populous city in the U.S. state of Pennsylvania and the List of United States cities by population, sixth-most populous city in the Unit ...

Scientific work

Pukánszky's early work concerned

von 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. It is a special type of C*-algebra. Von Neumann al ...

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

s. He found a geometric condition, known as the Pukánszky condition, that allowed an extension of the

orbit method In mathematics, the orbit method (also known as the Kirillov theory, the method of coadjoint orbits and by a few similar names) establishes a correspondence between irreducible unitary representations of a Lie group and its coadjoint orbits: orbit ...

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. 133 (1974), 81–137

References

Jacques Dixmier Jacques Dixmier (born 24 May 1924) is a French mathematician. He worked on operator algebras, especially C*-algebras, and wrote several of the standard reference books on them, and introduced the Dixmier trace and the Dixmier mapping. Biogra ...

, Michel Duflo,

András Hajnal András Hajnal (May 13, 1931 – July 30, 2016) was a professor of mathematics at Rutgers University and a member of the Hungarian Academy of Sciences known for his work in set theory and combinatorics. Biography Hajnal was born on 13 May 1931,< ...

Richard Kadison Richard Vincent Kadison (July 25, 1925 – August 22, 2018) was an American mathematician known for his contributions to the study of operator algebras. Career Born in New York City in 1925, Kadison was a Gustave C. Kuemmerle Professor in the De ...

Ádám Korányi Ádám Korányi (born July 13, 1932, in Szeged) is a Hungarian and American mathematician. He is a Distinguished Professor of Mathematics and Computer Science at Lehman College and the Graduate Center of the City University of New York. His resea ...

, Jonathan Rosenberg, and Michèle Vergne
Lajos Pukánszky (1928–1996)
Notices of the AMS, vol 45, number 4, April 1998, 492–499 *''The Orbit Method in Representation Theory, Copenhagen, 1988'', Progress in Mathematics, vol. 82, Birkhäuser Boston, Boston, MA, 1990 {{DEFAULTSORT:Pukanszky, lajos 1928 births 1996 deaths 20th-century Hungarian mathematicians Hungarian emigrants to the United States University of Pennsylvania faculty