The automorphisms of Petit's algebras

Let s 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 polynomial f ∈ K[t; σ] is invariant, and were first defined by Petit.

We compute all their automorphisms if s commutes with all automorphisms in AutF(K) and n ≥ m-1, where n is the order of σ and m the degree of f, and obtain partial results for n < m-1.

When K/F is a finite Galois field extension, we compute some automorphism groups. We also briefly investigate when two such algebras are isomorphic.

C. Brown < Christian.brown@nottingham.ac.uk >

S. Pumpluen < Susanne.pumpluen@nottingham.ac.uk >