The automorphisms of generalized cyclic Azumaya algebras
| Autor: | Susanne Pumplün |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Ring (mathematics)
Pure mathematics Algebra and Number Theory Rank (linear algebra) Rings and Algebras Polynomial ring 010102 general mathematics Mathematics::Rings and Algebras Order (ring theory) Center (group theory) Mathematics - Rings and Algebras Automorphism 01 natural sciences Mathematics::Group Theory Simple (abstract algebra) Mathematics::K-Theory and Homology Rings and Algebras (math.RA) Azumaya algebra Mathematics::Category Theory 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics |
| ISSN: | 0022-4049 |
| DOI: | 10.48550/arxiv.1904.12563 |
| Popis: | 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. Comment: 18 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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