Non-abelian group, in mathematics, a group that is not abelian (commutative)
Abelian | abelian | Non-abelian group | non-abelian group | Non-Abelian | non-abelian | Abelian group | Abelian and tauberian theorems |
See the books by Irving Kaplansky, László Fuchs, Phillip Griffith, and David Arnold, as well as the proceedings of the conferences on Abelian Group Theory published in Lecture Notes in Mathematics for more recent results.
Such a system is defined as Abelian and the ADT matrix is expressed in terms of an angle, (see Comment below), known also as the ADT angle.
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Since the treatment of the two-state case as presented in Diabatic raised numerous doubts we consider it here as a special case of the Non-Abelian case just discussed.
Friedrich Hermann Schottky (24 July 1851 – 12 August 1935) was a German mathematician who worked on elliptic, abelian, and theta functions and introduced Schottky groups and Schottky's theorem.
In any non-Abelian gauge theory, any maximum Abelian gauge is an incomplete gauge which fixes the gauge freedom outside of the maximum Abelian subgroup.
Hilbert class field, the maximal abelian unramified extension of a number field
Hyperelliptic functions were first published by Adolph Göpel (1812-1847) in his last paper Abelsche Transcendenten erster Ordnung (Abelian transcendents of first order) (in Journal für reine und angewandte Mathematik, vol. 35, 1847).
Mathematically, a Yang–Mills instanton is a self-dual or anti-self-dual connection in a principal bundle over a four-dimensional Riemannian manifold that plays the role of physical space-time in non-abelian gauge theory.
Wolfgang Krull (Über verallgemeinerte endliche Abelsche Gruppen, M. Z. 23 (1925) 161–196), returned to G.A. Miller's original problem of direct products of abelian groups by extending to abelian operator groups with ascending and descending chain conditions.
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of Math (1909)), for finite groups, though he mentions some credit is due to an earlier study of G.A. Miller where direct products of abelian groups were considered.
The link group of the Hopf link, the simplest non-trivial link – two circles, linked once – is the free abelian group on two generators, Note that the link group of two unlinked circles is the free nonabelian group on two generators, of which the free abelian group on two generators is a quotient.
More generally, given an abelian topological group G with Pontryagin dual G^, Parseval's theorem says the Pontryagin–Fourier transform is a unitary operator between Hilbert spaces L2(G) and L2(G^) (with integration being against the appropriately scaled Haar measures on the two groups.) When G is the unit circle T, G^ is the integers and this is the case discussed above.
In 1958 he was an invited speaker at the International Congress of Mathematicians in Edinburgh (on the topic of Some fundamental theorems on abelian function fields).
A more general subclass consists of the axisymmetric pp-waves, which in general have a two dimensional Abelian Lie algebra of Killing vector fields.
In its original form, it was applied to an unramified double covering of a Riemann surface, and was used by F. Schottky and H. W. E. Jung in relation with the Schottky problem, as it now called, of characterising Jacobian varieties among abelian varieties.
The scalar field is charged, and with an appropriate potential, it has the capacity to break the gauge symmetry via the Abelian Higgs mechanism.
The finite Thompson subgroup of a p-group, the subgroup generated by the abelian subgroups of maximal order.