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On the Brauer Group of Algebras Having a Grading and an Action

Published online by Cambridge University Press:  20 November 2018

Morris Orzech
Morris Orzech*
Affiliation:
The Institute for Advanced Study, Princeton, New Jersey
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Beginning with Wall's introduction [19] of Z2-graded central simple algebras over a field K, a number of related generalizations of the Brauer group have been proposed. In [16] the field K was replaced by a commutative ring R, building upon the theory developed in [1]. The concept of a G-graded central simple K-algebra (G an abelian group) was first defined in [12]; this work and that of [16] was subsequently unified in [6] and [7] via the construction and computation of the graded Brauer group Bφ﹛R, G) (φ a bilinear form from G X G to U(R), the units of R).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 3 , 01 June 1976 , pp. 533 - 552
Copyright
Copyright © Canadian Mathematical Society 1976

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