In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A...
7 KB (935 words) - 20:05, 12 January 2024
study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example...
16 KB (2,240 words) - 04:23, 17 March 2024
special orthogonal group SO(n), and the symplectic group Sp(2n). Simple algebraic groups and (more generally) semisimple algebraic groups are reductive. Claude...
55 KB (7,845 words) - 18:28, 24 April 2024
defined by polynomials, that is, that these are algebraic groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and Kolchin (1948)...
41 KB (6,000 words) - 20:12, 10 January 2024
Adele ring (redirect from Adelic)
global field (also adelic ring, ring of adeles or ring of adèles) is a central object of class field theory, a branch of algebraic number theory. It is...
87 KB (18,442 words) - 04:47, 12 January 2024
Idele group Idele class group Adelic algebraic group Global field Hasse principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class...
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Representation theory (section Linear algebraic groups)
technical value for dealing with the case that G is an algebraic group, treated as an adelic algebraic group. As a result, an entire philosophy, the Langlands...
55 KB (7,184 words) - 17:41, 8 July 2024
Automorphic form (category Lie groups)
algebraic group, treated as an adelic algebraic group. It does not completely include the automorphic form idea introduced above, in that the adelic approach...
13 KB (1,651 words) - 21:57, 9 March 2024
Congruence subgroup (redirect from Modular group Lambda)
integers. Given any algebraic group G {\displaystyle \mathbf {G} } over Q {\displaystyle \mathbb {Q} } the adelic algebraic group G ( A ) {\displaystyle...
27 KB (4,782 words) - 20:18, 14 June 2024
Tamagawa number (category Algebraic groups)
respect to the induced quotient measure. The Tamagawa measure on the adelic algebraic group G(A) is now defined as follows. Take a left-invariant n-form ω on...
7 KB (727 words) - 14:13, 16 December 2023