Richard A. Parker
Encyclopedia
Richard A. Parker is a mathematician and freelance computer programmer in Cambridge
, England
. He invented many of the algorithms for computing the modular character tables of finite simple group
s. He discovered the relation between Niemeier lattice
s and
deep holes of the Leech lattice
, and constructed Parker's Moufang loop
of order 213 (which was used by John Horton Conway
in his construction of the monster group
).
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, England
England
England is a country that is part of the United Kingdom. It shares land borders with Scotland to the north and Wales to the west; the Irish Sea is to the north west, the Celtic Sea to the south west, with the North Sea to the east and the English Channel to the south separating it from continental...
. He invented many of the algorithms for computing the modular character tables of finite simple group
Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, a normal subgroup and the quotient group, and the process can be repeated...
s. He discovered the relation between Niemeier lattice
Niemeier lattice
In mathematics, a Niemeier lattice is one of the 24positive definite even unimodular lattices of rank 24,which were classified by . gave a simplified proof of the classification. has a sentence mentioning that he found more than 10 such lattices, but gives no further details...
s and
deep holes of the Leech lattice
Leech lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space E24 found by .-History:Many of the cross-sections of the Leech lattice, including the Coxeter–Todd lattice and Barnes–Wall lattice, in 12 and 16 dimensions, were found much earlier than...
, and constructed Parker's Moufang loop
Moufang loop
In mathematics, a Moufang loop is a special kind of algebraic structure. It is similar to a group in many ways but need not be associative. Moufang loops were introduced by Ruth Moufang.-Definition:...
of order 213 (which was used by John Horton Conway
John Horton Conway
John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
in his construction of the monster group
Monster group
In the mathematical field of group theory, the Monster group M or F1 is a group of finite order:...
).
Books
- Conway, J. H.John Horton ConwayJohn Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
; Sloane, N. J. A.Neil SloaneNeil James Alexander Sloane is a British-U.S. mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing...
(1999). Sphere packings, lattices and groups. (3rd ed.) With additional contributions by E. Bannai, R. E. BorcherdsRichard BorcherdsRichard Ewen Borcherds is a British mathematician specializing in lattices, number theory, group theory, and infinite-dimensional algebras. He was awarded the Fields Medal in 1998.- Personal life :...
, John LeechJohn Leech (mathematician)John Leech was a British mathematician working in number theory, geometry and combinatorial group theory. He is best known for his discovery of the Leech lattice in 1965. He also discovered Ta in 1957...
, Simon P. NortonSimon P. NortonSimon Phillips Norton is a mathematician in Cambridge, England, who works on finite simple groups. He constructed the Harada–Norton group, and in 1979 together with John Conway proved there is a connection between the Monster group and the j-function in number theory. They dubbed this monstrous...
, A. M. OdlyzkoAndrew OdlyzkoAndrew Michael Odlyzko is a mathematician and a former head of the University of Minnesota's Digital Technology Center.In the field of mathematics he has published extensively on analytic number theory, computational number theory, cryptography, algorithms and computational complexity,...
, R. A. Parker, L. Queen and B. B. Venkov. Grundlehren der Mathematischen Wissenschaften, 290. New York: Springer-Verlag. ISBN 0-387-98585-9. - An Atlas of Brauer Characters (London Mathematical Society Monographs) by Christopher Jansen, Klaus Lux, Richard Parker, Robert Wilson. Oxford University Press, U.S. (October 1, 1995) ISBN 0-19-851481-6