Weyln.
/vʌɪl/ Mathematics.
Used attributively to designate various concepts introduced by Weyl.
a. Weyl group n. [translating French groupe de Weyl (C. Chevalley 1955, in Tohoku Math. Jrnl. 7 21)] a quotient group, important in the study of simple groups, constructed from two subgroups satisfying certain conditions, including that each generates the parent group and that their intersection is normal in one of them.
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the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > in abstract algebra > groups
syntheme1844
group1854
substitution group1861
quaternion group1881
subgroup1881
Abelian group1892
permutation group1893
quotient group1893
factor group1895
order1897
symmetric group1897
point group1903
Sylow subgroup1905
module1927
Lie group1939
symmetry group1956
Weyl group1961
stabilizer1965
1961 Amer. Jrnl. Math. 83 439 The Weyl group W of Σ is of order 12.
1971 Powell & Higman Finite Simple Groups iii. 136 The different copies of SL2 (k)..are permuted by the Weyl group of a root system attached to the semi-simple Lie algebra .
b. Weyl tensor n. [probably translating German Weyltensor] in general relativity, a tensor denoting that component of the curvature of space-time which is not determined locally by matter.
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the world > matter > physics > relativity > [noun] > tensor
tensor1916
Weyl tensor1962
1962 Jrnl. Math. Physics 3 569/1 The spinors ψ abcd, ϕ abc′d′, and Λ correspond, respectively, to the Weyl tensor, trace-free part of the Ricci tensor, and scalar curvature.
1979 Nature 23 Aug. 704/1 The Weyl tensor is a rough measure of gravitational clumping.
This entry has not yet been fully updated (first published 1993; most recently modified version published online September 2018).
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