The automorphisms of Petit's algebras

Brown, C. and Pumpluen, Susanne (2017) The automorphisms of Petit's algebras. Communications in Algebra . ISSN 1532-4125

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Abstract

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.

Item Type: Article
Keywords: Skew polynomial ring, skew polynomials, Ore polynomials, automorphisms, nonassociative algebras
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1080/00927872.2017.1327598
Depositing User: Eprints, Support
Date Deposited: 08 May 2017 13:50
Last Modified: 13 Oct 2017 00:51
URI: http://eprints.nottingham.ac.uk/id/eprint/42590

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