Azumaya algebras with general gradings and their automorphisms (Q1961897)

The author studies \(\Delta\)-graded Azumaya algebras in the sense of the reviewer, \textit{G. Garfinkel} and \textit{M. Orzech} [Trans. Am. Math. Soc. 175, 299-326 (1973; Zbl 0265.13002)], where \(\Delta\) is an additive Abelian group. In addition to developing, in somewhat different language, many of the results of [op. cit.], the author obtains two exact sequences involving the group \(\Aut_R(A)\) of automorphisms of the graded Azumaya \(R\)-algebra \(A\). These sequences generalize the Rosenberg-Zelinsky exact sequence \[ 1\to R^*\to A^*\to\Aut_R(A)\to\text{Pic}(R) \] for \(\Delta=0\), and results of \textit{H. Bass} [Lectures on topics in algebraic \(K\)-theory, Tata Institute of Fundamental Research Lectures on Mathematics and Physics 41 (1967; Zbl 0226.13006)] and \textit{C. Small} [Trans. Am. Math. Soc. 156, 455-491 (1971; Zbl 0216.32501)] when \(\Delta\) has order 2. (Also submitted to MR).