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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.
MSC:
17A35 Nonassociative division algebras
17A60 Structure theory for nonassociative algebras
16S36 Ordinary and skew polynomial rings and semigroup rings
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