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The monstrous moonshine is now known to be underlain by a vertex operator algebra called the moonshine module (or monster vertex algebra) constructed by Igor Frenkel, James Lepowsky, and Arne Meurman in 1988, which has the monster group as its group of symmetries.
The monster vertex algebra (or moonshine module) 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 ...
The monster vertex algebra ♮ (also called the "moonshine module") is the key to Borcherds's proof of the Monstrous moonshine conjectures. It was constructed by Frenkel, Lepowsky, and Meurman in 1988.
More remarkably, the Fourier coefficients for the positive exponents of q are the dimensions of the graded part of an infinite-dimensional graded algebra representation of the monster group called the moonshine module – specifically, the coefficient of q n is the dimension of grade-n part of the moonshine module, the first example being the ...
John K. S. McKay (18 November 1939 – 19 April 2022) [1] [2] was a British-Canadian mathematician and academic who worked at Concordia University, known for his discovery of monstrous moonshine, his joint construction of some sporadic simple groups, for the McKay conjecture in representation theory, and for the McKay correspondence relating certain finite groups to Lie groups.
The monster group is one of two principal constituents in the monstrous moonshine conjecture by Conway and Norton, [29] which relates discrete and non-discrete mathematics and was finally proved by Richard Borcherds in 1992.
Convicted of 16 'Monstrous' Killings. Stumpp was a farmer who lived in Bedbur, Germany during the late 1500s, according to the British Library, ...
Richard Ewen Borcherds (/ ˈ b ɔːr tʃ ər d z /; born 29 November 1959) [2] is a British [4] mathematician currently working in quantum field theory.He is known for his work in lattices, group theory, and infinite-dimensional algebras, [5] [6] for which he was awarded the Fields Medal in 1998.