Georgia Benkart
American mathematician (1947–2022)
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Education and career
Benkart received her BS degree in mathematics summa cum laude from the Ohio State University in 1970 and an MPhil in mathematics from Yale University in 1973. She completed her doctoral work at Yale under Nathan Jacobson and wrote a dissertation entitled Inner Ideals and the Structure of Lie Algebras. She was awarded a PhD in mathematics from the Yale University in 1974.
Upon completing her doctoral degree, Benkart began her long career at the University of Wisconsin–Madison, first as a MacDuffee Instructor and eventually as a E. B. Van Vleck Professor of Mathematics until she retired from teaching in 2006.
She held visiting positions at the Mathematical Sciences Research Institute in Berkeley, California, the Institute for Advanced Study in Princeton, New Jersey, the Aspen Center for Physics, and the University of Virginia. During her career, Benkart delivered over 350 invited talks including 3 plenary lectures at the Joint Mathematics Meetings and the Emmy Noether Lecture at the International Congress of Mathematicians in Seoul, South Korea in 2014.
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Personal life
Benkart was born on December 30, 1947, in Youngstown, Ohio, to George Benkart II and Florence K. Benkart. Her father served in the Army Corps of Engineers and her mother was a teacher in Youngstown's "ethnically rich south side."
Benkart died on April 29, 2022, aged 74, from undisclosed causes in Madison, Wisconsin. Her survivors included her sister, Paula Kaye Benkart.
Research
Benkart made a contribution to the classification of simple modular Lie algebras. Her work with J. Marshall Osborn on toroidal rank-one Lie algebras became one of the building blocks of the classification. The complete description of Hamiltonian Lie Algebras (with Gregory, Osborn, Strade, Wilson) can stand alone, and also has applications in the theory of pro-p groups.
In 2009, she published, jointly with Thomas Gregory and Alexander Premet, the first complete proof of the recognition theorem for graded Lie algebras in characteristics at least 5.
In the early 1990s, Benkart and Efim Zelmanov started to work on classification of root-graded Lie algebras and intersection matrix algebras. The latter were introduced by Peter Slodowy in his work on singularities. Berman and Moody recognized that these algebras (generalizations of affine Kac–Moody algebras) are universal root graded Lie algebras and classified them for simply laced root systems. Benkart and Zelmanov tackled the remaining cases involving the Freudenthal magic square and extended this square to exceptional Lie superalgebras.
Later Benkart extended these results in two directions. In a series of papers with Alberto Elduque she developed the theory of root graded Lie superalgebras. In a second series of works with Bruce Allison, Arturo Pianzola, Erhard Neher, et al. she determined the universal central covers of these algebras.
One of the pillars of the representation theory of quantum groups (and applications to combinatorics) is Masaki Kashiwara's theory of crystal bases. These are highly invariant bases which are well suited for decompositions of tensor products. In a paper with Seok-Jin Kang and Kashiwara, Benkart extended the theory of crystal bases to quantum superalgebras.
Benkart's work on noncommutative algebras related to algebraic combinatorics became a basic tool in the construction of tensor categories.
Service to the profession
Benkart served on several editorial boards including the boards of the American Mathematical Society for Surveys and Monographs and Abstracts, Communications in Algebra, and the Journal of Algebra. She served as the associate secretary of the American Mathematical Society for the Central Section from 2010 to 2020, and was a member of the governing council in 1995 and from 2010 to 2021. Benkart was active in the Association for Women in Mathematics (AWM) over many years, served as chair of the membership portfolio and the nominating committee, and helped plan the first AWM Research Symposium, which was also a celebration of the 40th anniversary of AWM.