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The automorphisms of generalized cyclic Azumaya algebras. (English) Zbl 07264653
Summary: We define a nonassociative generalization of cyclic Azumaya algebras employing skew polynomial rings \(D [t; \sigma]\), where \(D\) is an Azumaya algebra of constant rank with center \(C\) and \(\sigma\) an automorphism of \(D\), such that \(\sigma |_C\) has finite order. The automorphisms of these algebras are canonically induced by ring automorphisms of the skew polynomial ring \(D[t; \sigma]\) used in their construction. We achieve a description of their inner automorphisms. Results on the automorphisms of classical Azumaya algebras and central simple algebras of this type are obtained as special cases.
17A35 Nonassociative division algebras
17A60 Structure theory for nonassociative algebras
16S36 Ordinary and skew polynomial rings and semigroup rings
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