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...

study of algebraic groups belongs both to algebraic geometry and group theory. Many groups of geometric transformations are algebraic groups; for example...

special orthogonal group SO(n), and the symplectic group Sp(2n). Simple algebraic groups and (more generally) semisimple algebraic groups are reductive. Claude...

defined by polynomials, that is, that these are algebraic groups. The founders of the theory of algebraic groups include Maurer, Chevalley, and Kolchin (1948)...

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...

Idele group Idele class group Adelic algebraic group Global field Hasse principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class...

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...

algebraic group, treated as an adelic algebraic group. It does not completely include the automorphic form idea introduced above, in that the adelic approach...

integers. Given any algebraic group G {\displaystyle \mathbf {G} } over Q {\displaystyle \mathbb {Q} } the adelic algebraic group G ( A ) {\displaystyle...

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...