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Armand Borel was a Swiss mathematician, born in La Chaux-de-Fonds, and was a permanent professor at the Institute for Advanced Study in Princeton, New Jersey, United States from 1957 to 1993. He worked in algebraic topology, in the theory of Lie groups, and was one of the creators of the contemporary theory of linear algebraic groups.
In abstract algebra, a Jordan algebra is a nonassociative algebra over a field whose multiplication satisfies the following axioms:
- .
In mathematics, the monster Lie algebra is an infinite-dimensional generalized Kac–Moody algebra acted on by the monster group, which was used to prove the monstrous moonshine conjectures.
In mathematics, an Albert algebra is a 27-dimensional exceptional Jordan algebra. They are named after Abraham Adrian Albert, who pioneered the study of non-associative algebras, usually working over the real numbers. Over the real numbers, there are three such Jordan algebras up to isomorphism. One of them, which was first mentioned by Pascual Jordan, John von Neumann, and Eugene Wigner (1934) and studied by Albert (1934), is the set of 3×3 self-adjoint matrices over the octonions, equipped with the binary operation
In mathematics, the Bruhat order is a partial order on the elements of a Coxeter group, that corresponds to the inclusion order on Schubert varieties.
In representation theory, a Yangian is an infinite-dimensional Hopf algebra, a type of a quantum group. Yangians first appeared in physics in the work of Ludvig Faddeev and his school in the late 1970s and early 1980s concerning the quantum inverse scattering method. The name Yangian was introduced by Vladimir Drinfeld in 1985 in honor of C.N. Yang.
Ellis Robert Kolchin was an American mathematician at Columbia University. Kolchin earned a doctorate in mathematics from Columbia University in 1941 under supervision of Joseph Ritt. He was awarded a Guggenheim Fellowship in 1954 and 1961.
Edward Vladimirovich Frenkel is a Russian-American mathematician working in representation theory, algebraic geometry, and mathematical physics. He is a professor of mathematics at University of California, Berkeley, member of the American Academy of Arts and Sciences, and author of the bestselling book Love and Math.
In mathematics, a chiral algebra is an algebraic structure introduced by Beilinson & Drinfeld (2004) as a rigorous version of the rather vague concept of a chiral algebra in physics.
In algebra, a Jantzen filtration is a filtration of a Verma module of a semisimple Lie algebra, or a Weyl module of a reductive algebraic group of positive characteristic. Jantzen filtrations were introduced by Jantzen (1979).
Jens Carsten Jantzen is a mathematician working on representation theory and algebraic groups, who introduced the Jantzen filtration, the Jantzen sum formula, and translation functors.
In mathematics, a Manin triple consists of a Lie algebra g with a non-degenerate invariant symmetric bilinear form, together with two isotropic subalgebras p and q such that g is the direct sum of p and q as a vector space.
In mathematics, a quadratic-linear algebra is an algebra over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators. They were introduced by Polishchuk and Positselski (2005, p.101). An example is the universal enveloping algebra of a Lie algebra, with generators a basis of the Lie algebra and relations of the form XY – YX – [X, Y] = 0.
In mathematics, a Tate vector space is a vector space obtained from finite-dimensional vector spaces in a way that makes it possible to extend concepts such as dimension and determinant to an infinite-dimensional situation. Tate spaces were introduced by Alexander Beilinson, Boris Feigin, and Barry Mazur (1991), who named them after John Tate.
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.
In mathematics, chiral homology, introduced by Alexander Beilinson and Vladimir Drinfeld, is, in their words, "a “quantum” version of the space of global horizontal sections of an affine -scheme ."
In mathematics, the Ran space of a topological space X is a topological space whose underlying set is the set of all nonempty finite subsets of X: for a metric space X the topology is induced by the Hausdorff distance. The notion is named after Ziv Ran. It seems the notion was first introduced and popularized by Alexander Beilinson and Vladimir Drinfeld in the context of Chiral algebras.
Dmitry Borisovich Fuchs is a Russian-American mathematician, specializing in the representation theory of infinite-dimensional Lie groups and in topology.
References
- Beilinson, Alexander; Drinfeld, Vladimir (2004), Chiral algebras, American Mathematical Society Colloquium Publications, 51, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3528-9, MR 2058353
- Kac, Victor (1998), Vertex algebras for beginners, University Lecture Series, 10 (2nd ed.), Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1396-6, MR 1651389
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
The International Standard Book Number (ISBN) is a numeric commercial book identifier which is intended to be unique. Publishers purchase ISBNs from an affiliate of the International ISBN Agency.
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