James Edward Humphreys (December 10, 1939 – August 27, 2020) was an American mathematician, who worked in
algebraic group
In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory.
Man ...
s,
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, and
Lie algebra
In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an Binary operation, operation called the Lie bracket, an Alternating multilinear map, alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow ...
s and applications of these mathematical structures. He is known as the author of several mathematical texts, such as ''Introduction to Lie Algebras and Representation Theory'' and ''Reflection Groups and Coxeter Groups''.
Humphreys died weeks after contracting
COVID-19
Coronavirus disease 2019 (COVID-19) is a contagious disease caused by a virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first known case was COVID-19 pandemic in Hubei, identified in Wuhan, China, in December ...
during the
COVID-19 pandemic in Massachusetts
The COVID-19 pandemic in Massachusetts is part of an ongoing pandemic of coronavirus disease 2019 (COVID-19) in the U.S. state of Massachusetts. The first confirmed case was reported on February 1, 2020, and the number of cases began increasi ...
.
Education
Humphreys attended elementary and secondary school in Erie, Pennsylvania and then studied at
Oberlin College
Oberlin College is a Private university, private Liberal arts colleges in the United States, liberal arts college and conservatory of music in Oberlin, Ohio. It is the oldest Mixed-sex education, coeducational liberal arts college in the United S ...
(bachelor's degree 1961) and from 1961 philosophy and mathematics at
Cornell University
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...
. At
Yale University
Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the wo ...
he earned his master's degree in 1964 and his PhD in 1966 under
George Seligman
George Benham Seligman (born April 30, 1927) is an American mathematician who works on Lie algebras, especially semi-simple Lie algebras.
Biography
Seligman received his bachelor's degree in 1950 from the University of Rochester and his PhD in ...
with thesis ''Algebraic Lie Algebras over fields of prime characteristic''.
Career
In 1966, he became an assistant professor at the
University of Oregon
The University of Oregon (UO, U of O or Oregon) is a public research university in Eugene, Oregon. Founded in 1876, the institution is well known for its strong ties to the sports apparel and marketing firm Nike, Inc, and its co-founder, billion ...
and in 1970 an associate professor at
New York University
New York University (NYU) is a private research university in New York City. Chartered in 1831 by the New York State Legislature, NYU was founded by a group of New Yorkers led by then-Secretary of the Treasury Albert Gallatin.
In 1832, the ...
. At the
University of Massachusetts Amherst
The University of Massachusetts Amherst (UMass Amherst, UMass) is a public research university in Amherst, Massachusetts and the sole public land-grant university in Commonwealth of Massachusetts. Founded in 1863 as an agricultural college, it ...
he became in 1974 an associate professor and in 1976 a full professor; he retired there in 2003 as professor emeritus. In 1968/69 and in 1977, he was a visiting scholar at the
Institute for Advanced Study
The Institute for Advanced Study (IAS), located in Princeton, New Jersey, in the United States, is an independent center for theoretical research and intellectual inquiry. It has served as the academic home of internationally preeminent scholar ...
and in 1969/70 at the
Courant Institute of Mathematical Sciences
The Courant Institute of Mathematical Sciences (commonly known as Courant or CIMS) is the mathematics research school of New York University (NYU), and is among the most prestigious mathematics schools and mathematical sciences research cente ...
of New York University. In 1985 he was a visiting professor at
Rutgers University
Rutgers University (; RU), officially Rutgers, The State University of New Jersey, is a Public university, public land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's ...
.
Works
*Arithmetic Groups,
Lecture Notes in Mathematics
''Lecture Notes in Mathematics'' is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Spr ...
789, Springer Verlag 1980 (from lectures at the Courant Institute 1971)
Conjugacy classes in semisimple algebraic groups AMS 1995
Springer Verlag,
Graduate Texts in Mathematics
Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag. The books in this series, like the other Springer-Verlag mathematics series, are yellow books of a standard s ...
, 1972, 7th edition 1997 (also translated into Chinese and Russian)
*Linear Algebraic Groups, Graduate Texts in Mathematics,
Springer Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
Originally founded in 1842 in ...
1974, 1998 (also translated into Russian).
*Ordinary and modular representations of Chevalley groups, Springer Verlag 1976.
*Modular representations of finite groups of Lie type, London Mathematical Society Lecture Note Series 326,
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press
A university press is an academic publishing hou ...
2006
Reflection Groups and Coxeter Groups Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press
A university press is an academic publishing hou ...
1990.
Representations of semisimple Lie algebras in the BGG category AMS 2008
*Modular representations of simple Lie algebras, Bull. Amer. Math. Soc. (N.S.), Vol. 35, 1998, pp. 105–122.
*Modular representations of classical Lie algebras, Bull. Amer. Math. Soc., Vol. 76, 1970, 878–882
''Algebraic groups and modular Lie algebras'' Memoirs AMS 71, 1967
*Hilbert's fourteenth problem,
American Mathematical Monthly
''The American Mathematical Monthly'' is a mathematical journal founded by Benjamin Finkel in 1894. It is published ten times each year by Taylor & Francis for the Mathematical Association of America.
The ''American Mathematical Monthly'' is an e ...
, Vol. 85, 1978, 341–353
*Representations of
, Amer. Math. Monthly, Vol. 82, 1975, 21–39
*Highest weight modules for semisimple Lie algebras, in: Representation Theory I,
Lecture Notes in Mathematics
''Lecture Notes in Mathematics'' is a book series in the field of mathematics, including articles related to both research and teaching. It was established in 1964 and was edited by A. Dold, Heidelberg and B. Eckmann, Zürich. Its publisher is Spr ...
831, Springer Verlag 1980, pp, 72–103
Awards
Humphreys received the
Lester R. Ford Award
Lester is an ancient Anglo-Saxon surname and given name. Notable people and characters with the name include:
People
Given name
* Lester Bangs (1948–1982), American music critic
* Lester W. Bentley (1908–1972), American artist from Wisc ...
for the publication ''Representations of
'' in 1976.
References
External links
Homepage
{{DEFAULTSORT:Humphreys, James E.
1939 births
20th-century American mathematicians
21st-century American mathematicians
Oberlin College alumni
Yale University alumni
University of Massachusetts Amherst faculty
People from Erie, Pennsylvania
Institute for Advanced Study visiting scholars
2020 deaths
Cornell University alumni
LGBT people from Massachusetts
Deaths from the COVID-19 pandemic in Massachusetts
Mathematicians from Pennsylvania