A bigger Brauer group

The Bigger Brauer Group Is Really Big

I show that each étale n-cohomology class on noetherian schemes comes from a Čech cocycle, provided that any n-tuple of points admits an affine open neighborhood. Together with results of Raeburn and Taylor on the bigger Brauer group, this implies that for schemes such that each pair of points admits an affine open neighborhood, any étale Gm-gerbe comes from a coherent central separable algebra...

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 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...

The Differential Brauer Group

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.