The Brauer group of an affine cone

Brauer Algebras and the Brauer Group

An algebra is a vector space V over a field k together with a kbilinear product of vectors under which V is a ring. A certain class of algebras, called Brauer algebras algebras which split over a finite Galois extension appear in many subfields of abstract algebra, including K-theory and class field theory. Beginning with a definition of the the tensor product, we define and study Brauer algebr...

The Differential Brauer Group

The Equivariant Brauer Group of a Group

We consider the Brauer group BM(k, G) of a group G (finite or infinite) over a commutative ring k with identity. A split exact sequence 1 −→ Br′(k) −→ BM′(k, G) −→ Gal(k, G) −→ 1 is obtained. This generalizes the Fröhlich-Wall exact sequence ([7, 8])from the case of a field to the case of a commutative ring, and generalizes the PiccoPlatzeck exact sequence ([13]) from the finite case of G to th...

Groupoids and the Brauer Group

Using a groupoid of matrix subalgebras in a fixed matrix algebra we define some nonabelian bundle gerbe which probably gives rise to some new twistings in K-theory.

The Brauer Group of a Hopf Algebra

Let H be a Hopf algebra with a bijective antipode over a commutative ring k with unit. The Brauer group of H is defined as the Brauer group of Yetter–Drinfel’d H-module algebras, which generalizes the Brauer–Long group of a commutative and cocommutative Hopf algebra and those known Brauer groups of structured algebras.