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James Edward Humphreys (December 10, 1939 – August 27, 2020) was an American mathematician, who worked in algebraic groups,
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 addit ...
s, and
Lie algebra In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi iden ...
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 identified in Wuhan, China, in December 2019. The disease quickl ...
during the COVID-19 pandemic in Massachusetts.


Education

Humphreys attended elementary and secondary school in Erie, Pennsylvania and then studied at Oberlin College (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 ...
. At
Yale University Yale University is a Private university, private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the List of Colonial Colleges, third-oldest institution of higher education in the United Sta ...
he earned his master's degree in 1964 and his PhD in 1966 under George Seligman 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, ...
. 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 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 land-grant research university consisting of four campuses in New Jersey. Chartered in 1766, Rutgers was originally called Queen's College, and wa ...
.


Works

*Arithmetic Groups, Lecture Notes in Mathematics 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 standa ...
, 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 in the world. It is also the King's Printer. Cambr ...
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 in the world. It is also the King's Printer. Cambr ...
1990.
Representations of semisimple Lie algebras in the BGG category \mathcal O
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 ...
, Vol. 85, 1978, 341–353 *Representations of \operatorname(2,p), Amer. Math. Monthly, Vol. 82, 1975, 21–39 *Highest weight modules for semisimple Lie algebras, in: Representation Theory I, Lecture Notes in Mathematics 831, Springer Verlag 1980, pp, 72–103


Awards

Humphreys received the Lester R. Ford Award for the publication ''Representations of \operatorname(2,p)'' in 1976.


References


External links


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{{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