Brauer group of a linear algebraic 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...

On the Brauer Group of Real Algebraic Surfaces

Let X be a real projective algebraic manifold, s numerates connected components of X(R) and 2Br(X) the subgroup of elements of order 2 of cohomological Brauer group Br(X). We study the natural homomorphism ξ :2 Br(X) → (Z/2)s and prove that ξ is epimorphic if H(X(C)/G;Z/2) → H(X(R);Z/2) is injective. Here G = Gal(C/R). For an algebraic surface X with H(X(C)/G;Z/2) = 0 and X(R) 6= ∅, we give a f...

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 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.