Sentence examples for abelian from inspiring English sources
noun
A member of a sect in fourth-century Africa mentioned by St. Augustine, who states that they married but lived in continence after the manner, as they claimed, of Abel.
In 1984 he became a professor at the Institute for Advanced Study, Princeton, New Jersey, U.S. In 1949 the French mathematician André Weil made a series of conjectures concerning zeta functions of curves of abelian varieties.
Hermite was a major figure in the development of the theory of algebraic forms, the arithmetical theory of quadratic forms, and the theories of elliptic and Abelian functions.
Among them are the theory of polynomial equations with Abelian groups.
The elements in an abelian group are commutative, which means that changing the order of the elements for a particular mathematical operation does not affect the result (eg, 1 + 2 is the same as 2 + 1).
This is one of a whole series of jokes, such as: "What's purple, dangerous and commutes?" The answers is: "An abelian grape with a machine gun".
This allowed him to retain the normal rules of algebra except for the commutative law for multiplication (in general, ab ≠ ba), so that the quaternions only form an associative group—in particular, a non-Abelian group.
Noting Weyl's strong association of gauge invariance with relativity theory in Weyl's 1929 paper, Yang (1986) remarks: "Twenty years later, when Mills and I worked on non-Abelian gauge fields, our motivation was completely divorced from general relativity and we did not appreciate that gauge fields and general relativity are somehow related.
Only in the late 1960's did I recognize the structural similarity mathematically of non-Abelian gauge fields with general relativity and understand that they both were connections mathematically".
New theoretical concepts had to be introduced, mainly connected with non-Abelian gauge theories and spontaneous symmetry breaking.
The main steps in development of gauge theory are the Yang and Mills non-Abelian gauge theory of 1954, and the problems and solutions associated with the successful development of gauge theories for the short-range weak and strong interactions.
