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 algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

of solvable

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

s. He was born in

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

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

University of Szeged , mottoeng = Truth. Bravery. Freedom. , established = , type = Public research university , founder = Emperor Franz Joseph I , affiliation = European University Association, Science Without Borders, Confucius Institute , budget = US$220 mi ...

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 land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of Mary ...

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...

UCLA The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

), in 1965 he became a professor at the

University of Pennsylvania The University of Pennsylvania (also known as Penn or UPenn) is a private research university in Philadelphia. It is the fourth-oldest institution of higher education in the United States and is ranked among the highest-regarded universitie ...

, where he stayed until his retirement. He gave an

invited address at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

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 ( da, Københavns Universitet, KU) is a prestigious public university, public research university in Copenhagen, Copenhagen, Denmark. Founded in 1479, the University of Copenhagen is the second-oldest university in ...

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

Philadelphia Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...

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 algeb ...

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: or ...

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 Mathematica'' is a peer-reviewed open-access scientific journal covering research in all fields of mathematics. According to Cédric Villani, this journal is "considered by many to be the most prestigious of all mathematical research jo ...

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 Michel Duflo (born 15 August 1943) is a French mathematician who works in the representation theory of Lie groups. Life From 1962, Duflo studied at the École normale supérieure and received a doctorate under the supervision of Jacques Dixm ...

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)F ...

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, City University of New York and at the CUNY Graduate Center. His ...

, 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