Equivalence and the Brauer–Clifford Group for G-Algebras over Commutative Rings

Abstract

The notion of G-algebra equivalence for a group G is generalized from the setting of G-algebras over fields to G-algebras over commutative rings. This leads to a formulation of Turull's Brauer–Clifford group for separable G-algebras over commutative rings, and to connections with Fröhlich and Wall's equivariant Brauer group.

Key Words:

• Brauer–Clifford group
• Equivariant Brauer group
• G-algebras

2000 Mathematics Subject Classification:

• Primary 13A20
• Secondary 16A16, 12G05, 20C10

ACKNOWLEDGMENT

The work of the first author was supported by NSERC.

Notes

Communicated by S. Sehgal.