Geodesic
Automorphisms of G-Azumaya Algebras
Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1047-1058

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a commutative ring, G a finite abelian group of order n and exponent m, and assume n is a unit in R. In [10], F. W. Long defined a generalized Brauer group, BD(R, G), of algebras with a G-action and G-grading, whose elements are equivalence classes of G-Azumaya algebras. In this paper we investigate the automorphisms of a G-Azumaya algebra A and prove that if Picm (R) is trivial, then these automorphisms are all, in some sense, inner.In fact, each of these “inner” automorphisms can be written as the composition of an inner automorphism in the usual sense and a “linear“ automorphism, i.e., an automorphism of the type with r(σ) a unit in R. We then use these results to show that the group of gradings of the centre of a G-Azumaya algebra A is a direct summand of G, and thus if G is cyclic of order pr, A is the (smash) product of a commutative and a central G-Azumaya algebra. 
Beattie, Margaret. Automorphisms of G-Azumaya Algebras. Canadian journal of mathematics, Tome 37 (1985) no. 6, pp. 1047-1058. doi: 10.4153/CJM-1985-056-7
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