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...

In mathematics, the Brauer–Wall group or super Brauer group or graded Brauer group for a field F is a group BW(F) classifying finite-dimensional graded...

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...

are also named after Richard Brauer because of their close relation to the Brauer group. In dimension one, the Severi–Brauer varieties are conics. The corresponding...

historical proofs. The theorem is essentially equivalent to saying that the Brauer group of a finite field is trivial. In fact, this characterization immediately...

{\displaystyle [A][B]=\left[A\otimes _{k}B\right]} form an abelian group called the Brauer group of k and is denoted by Br(k). By the Artin–Wedderburn theorem...

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...

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

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

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...

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)...

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...

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...

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...

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...

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...

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...

Then A is isomorphic to the matrix algebra Md(K). Using the theory of Brauer group, one shows that two central simple algebras A and B over an algebraic...

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...

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...

example, the Brauer group, which is classically defined as the group of central simple F-algebras, can be reinterpreted as a Galois cohomology group, namely...

Brauer's main theorems are three theorems in representation theory of finite groups linking the blocks of a finite group (in characteristic p) with those...

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...

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....

classical theory was found in the shape of the Grothendieck version of the Brauer group; this was applied in short order to diophantine geometry, by Yuri Manin...

mathematics, a Brauer algebra is an associative algebra introduced by Richard Brauer in the context of the representation theory of the orthogonal group. It plays...

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...

algebras to compute the Brauer group of a global field. Subsequently, Tate introduced what are now known as Tate cohomology groups. In the decades following...

again fall into multiple groups. One group favors a serif design which is derived from the main serif font: [...] Another group favor a sans-serif design...