The automorphisms of Petit's algebras
Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t; σ]=fK[t; σ] obtained when the twisted polynomialf 2 K[t; σ] is invariant, and were first defined by Pet...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis
2017
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| Online Access: | https://eprints.nottingham.ac.uk/42590/ |
| _version_ | 1848796520513536000 |
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| author | Brown, C. Pumpluen, Susanne |
| author_facet | Brown, C. Pumpluen, Susanne |
| author_sort | Brown, C. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t; σ]=fK[t; σ] obtained when the twisted polynomialf 2 K[t; σ] is invariant, and were first defined by Petit. We compute all their automorphisms if V commutes with all automorphisms in AutF (K) and n < m-1. In thecase where K=F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic. |
| first_indexed | 2025-11-14T19:49:17Z |
| format | Article |
| id | nottingham-42590 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T19:49:17Z |
| publishDate | 2017 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-425902018-05-17T17:03:14Z https://eprints.nottingham.ac.uk/42590/ The automorphisms of Petit's algebras Brown, C. Pumpluen, Susanne Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t; σ]=fK[t; σ] obtained when the twisted polynomialf 2 K[t; σ] is invariant, and were first defined by Petit. We compute all their automorphisms if V commutes with all automorphisms in AutF (K) and n < m-1. In thecase where K=F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic. Taylor & Francis 2017-05-16 Article PeerReviewed application/pdf en https://eprints.nottingham.ac.uk/42590/1/Galoisexts.pdf Brown, C. and Pumpluen, Susanne (2017) The automorphisms of Petit's algebras. Communications in Algebra . ISSN 1532-4125 Skew polynomial ring skew polynomials Ore polynomials automorphisms nonassociative algebras http://www.tandfonline.com/eprint/YSQzP3Np7vXecxVj8JUc/full doi:10.1080/00927872.2017.1327598 doi:10.1080/00927872.2017.1327598 |
| spellingShingle | Skew polynomial ring skew polynomials Ore polynomials automorphisms nonassociative algebras Brown, C. Pumpluen, Susanne The automorphisms of Petit's algebras |
| title | The automorphisms of Petit's algebras |
| title_full | The automorphisms of Petit's algebras |
| title_fullStr | The automorphisms of Petit's algebras |
| title_full_unstemmed | The automorphisms of Petit's algebras |
| title_short | The automorphisms of Petit's algebras |
| title_sort | automorphisms of petit's algebras |
| topic | Skew polynomial ring skew polynomials Ore polynomials automorphisms nonassociative algebras |
| url | https://eprints.nottingham.ac.uk/42590/ https://eprints.nottingham.ac.uk/42590/ https://eprints.nottingham.ac.uk/42590/ |