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In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order
246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
= 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
≈ 8×1053.
Richard Ewen Borcherds is a British mathematician currently working in quantum field theory. He is known for his work in lattices, group theory, and infinite-dimensional algebras, for which he was awarded the Fields Medal in 1998.
In the area of modern algebra known as group theory, the baby monster groupB (or, more simply, the baby monster) is a sporadic simple group of order
In the area of modern algebra known as group theory, the Thompson groupTh is a sporadic simple group of order
In mathematics, monstrous moonshine, or moonshine theory, is the unexpected connection between the monster group M and modular functions, in particular, the j function. The initial numerical observation was made by John McKay in 1978, and the phrase was coined by John Conway and Simon P. Norton in 1979.
In mathematics, and in particular in the mathematical background of string theory, the Goddard–Thorn theorem is a theorem describing properties of a functor that quantizes bosonic strings. It is named after Peter Goddard and Charles Thorn.
In mathematics, a vertex operator algebra (VOA) is an algebraic structure that plays an important role in two-dimensional conformal field theory and string theory. In addition to physical applications, vertex operator algebras have proven useful in purely mathematical contexts such as monstrous moonshine and the geometric Langlands correspondence.
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 autonomous category is a monoidal category where dual objects exist.
Robert Arnott Wilson is a retired mathematician in London, England, who is best known for his work on classifying the maximal subgroups of finite simple groups and for the work in the Monster group. He is also an accomplished violin, viola and piano player, having played as the principal viola in the Sinfonia of Birmingham. Due to a damaged finger, he now principally plays the kora.
The monster vertex algebra is a vertex algebra acted on by the monster group that was constructed by Igor Frenkel, James Lepowsky, and Arne Meurman. R. Borcherds used it to prove the monstrous moonshine conjectures, by applying the Goddard–Thorn theorem of string theory to construct the monster Lie algebra, an infinite-dimensional generalized Kac–Moody algebra acted on by the monster.
Igor Borisovich Frenkel is a Russian-American mathematician at Yale University working in representation theory and mathematical physics.
James Lepowsky is a professor of mathematics at Rutgers University, New Jersey. Previously he taught at Yale University. He received his Ph.D. from Massachusetts Institute of Technology in 1970 where his advisors were Bertram Kostant and Sigurdur Helgason. Lepowsky graduated from Stuyvesant High School in 1961, 16 years after Kostant. His current research is in the areas of infinite-dimensional Lie algebras and vertex algebras. He has written several books on vertex algebras and related topics. In 1988, in a joint work with Igor Frenkel and Arne Meurman, he constructed the monster vertex algebra. His PhD students include Stefano Capparelli, Yi-Zhi Huang, Haisheng Li, Arne Meurman, and Antun Milas.
Robert Louis Griess, Jr. is a mathematician working on finite simple groups and vertex algebras. He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan.
In mathematical physics the Knizhnik–Zamolodchikov equations, or KZ equations, are linear differential equations satisfied by the correlation functions of two-dimensional conformal field theories associated with an affine Lie algebra at a fixed level. They form a system of complex partial differential equations with regular singular points satisfied by the N-point functions of affine primary fields and can be derived using either the formalism of Lie algebras or that of vertex algebras.
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, a 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 Chiral Algebras, Beilinson and Drinfeld introduced the notion of chiral algebra, which based on the pseudo-tensor category of D-modules. They give an 'coordinate independent' notion of vertex algebras, which are based on formal power series. Chiral algebras on curves are essentially conformal vertex algebras.
In mathematics, umbral moonshine is a mysterious connection between Niemeier lattices and Ramanujan's mock theta functions. It is a generalization of the Mathieu moonshine phenomenon connecting representations of the Mathieu group M24 with K3 surfaces.
Julius Bogdan Borcea was a Romanian Swedish mathematician. His scientific work included vertex operator algebra and zero distribution of polynomials and entire functions, via correlation inequalities and statistical mechanics.
Howard Garland is an American mathematician, who works on algebraic groups, Lie algebras, and infinite-dimensional algebras.
References
- ↑ Ogg, Andrew (1991). "Review: Vertex operator algebras and the Monster". Bull. Amer. Math. Soc. (N.S.). 25 (2): 425–432. doi: 10.1090/s0273-0979-1991-16086-6 .
