Georgia Benkart
| Georgia Benkart | |
|---|---|
| Born | 1949 Youngstown, Ohio, U.S. |
| Nationality | American |
| Alma mater | B.S., Ohio State University, 1970 Ph.D., Yale University, 1974 |
| Known for | Classification of simple modular Lie algebras |
| Awards |
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| Scientific career | |
| Fields | Lie algebras, Representation Theory, Combinatorics |
| Institutions | University of Wisconsin–Madison |
| Doctoral advisor | Nathan Jacobson |
Georgia McClure Benkart is an American mathematician who is known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She has published over 100 journal articles and co-authored 3 American Mathematical Society Memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures. Benkart's role as a teacher has led to her work in mentoring 22 doctoral students.
Benkart made a contribution to the classification of simple modular Lie algebras. Her work with J. M. 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 T. Gregory and A. Premet, the first complete proof of the recognition theorem for graded Lie algebras in characteristics at least 5.
In the early 90s Benkart and Efim Zelmanov started to work on classification of root-graded Lie algebras and intersection matrix algebras. The latter were introduced by P. 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 so-called Magic Freudenthal–Tits “Square” and extended this square to exceptional Lie superalgebras.
Later Benkart extended these results in two directions. In a series of papers with A. Elduque she developed the theory of root graded Lie superalgebras. In a second series of works with B. Allison, A. Pianzola, E. 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 Kashiwara's theory of crystal bases. These are highly invariant bases which are well suited for decompositions of tensor products. In a paper with S.-J. Kang and M. 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.
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