The automorphisms of Petit's algebras

Brown, C.; Pumpluen, Susanne

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.

Citation

Brown, C., & Pumpluen, S. (in press). The automorphisms of Petit's algebras. Communications in Algebra, https://doi.org/10.1080/00927872.2017.1327598

• Journal Article Type: Article
• Acceptance Date: Apr 30, 2017
• Online Publication Date: May 16, 2017
• Deposit Date: May 8, 2017
• Publicly Available Date: May 16, 2017
• Journal: Communications in Algebra
• Print ISSN: 0092-7872
• Electronic ISSN: 1532-4125
• Publisher: Taylor and Francis
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1080/00927872.2017.1327598
• Keywords: Skew polynomial ring, skew polynomials, Ore polynomials, automorphisms, nonassociative algebras
• Public URL: https://nottingham-repository.worktribe.com/output/860496
• Publisher URL: http://www.tandfonline.com/eprint/YSQzP3Np7vXecxVj8JUc/full
• Contract Date: May 8, 2017