Brauer–Wall group


In mathematics, the Brauer–Wall group or super Brauer group or graded Brauer group for a field F is a group BW classifying finite-dimensional graded central division algebras over the field. It was first defined by as a generalization of the Brauer group.
The Brauer group of a field F is the set of the similarity classes of finite dimensional central simple algebras over F under the operation of tensor product, where two algebras are called similar if the commutants of their simple modules are isomorphic. Every similarity class contains a unique division algebra, so the elements of the Brauer group can also be identified with isomorphism classes of finite dimensional central division algebras. The analogous construction for Z/2Z-graded algebras defines the Brauer–Wall group BW.

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