Brauer group information

In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with...

CSA over the real numbers is Brauer equivalent to either the real numbers or the quaternions. Explicitly, the Brauer group of the real numbers consists...

Alexander Grothendieck made it the basis for his geometric theory of the Brauer group in Bourbaki seminars from 1964–65. There are now several points of access...

the algebraist Richard Brauer. The group may also be defined in terms of Galois cohomology. More generally, the Brauer group of a scheme is defined in...

holding for cubic forms can be tied into the theory of the Brauer group; this is the Brauer–Manin obstruction, which accounts completely for the failure...

combinatorics and number theory. Within finite group theory, character-theoretic results proved by Richard Brauer using modular representation theory played...

that the groups H2(E/F) are all subgroups of the Brauer group. In local class field theory the Brauer groups are the same as Brauer groups of fields...

Richard Dagobert Brauer (February 10, 1901 – April 17, 1977) was a leading German and American mathematician. He worked mainly in abstract algebra, but...

CSA over R, and in fact represent the only non-trivial element of the Brauer group of the reals (see below). Given two central simple algebras A ~ M(n,S)...

Brandt Brauer Frick is a German electronic music ensemble from Berlin. The group's members are Daniel Brandt, Jan Brauer, and Paul Frick. The group's members...

Otto Schreier's 1926 treatment, and in Richard Brauer's 1928 study of simple algebras and the Brauer group. A fuller discussion of this history may be found...

The Manin obstruction is sometimes called the Brauer–Manin obstruction, as Manin used the Brauer group of X to define it. For abelian varieties the Manin...

invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes from Helmut Hasse and Ernst Witt....

theory of finite groups, a Brauer tree is a tree that encodes the characters of a block with cyclic defect group of a finite group. In fact, the trees...

Michael H. Brauer is an American mix engineer. He received a Grammy for "Best Pop Vocal Album" for his work on John Mayer's Continuum, "Best Alternative...

the 1920s. The case of 2-cocycles for the multiplicative group is that of the Brauer group, and the implications seem to have been well known to algebraists...

order two in the Brauer group of F. For some fields, including algebraic number fields, every element of order 2 in its Brauer group is represented by...

is again a well-defined function on Witt classes with values in the Brauer group of the field of definition. We define a ring over K, Q(K), as a set of...

ij=-ji=k} . In this case the algebra represents an element of order 2 in the Brauer group of K, which is identified with -1 if it is a division algebra and +1...

F and which are finite-dimensional over F can be turned into a group, the Brauer group of the field F. One way to construct finite-dimensional associative...