On trace forms of higher degree Original Research Article

Let A be a central simple algebra over a field k, and let tr denote its reduced trace. Then ψd(X) = tr Xd is the trace form of degree d on A. A similarity of (A, ψd) is a linear map f:A → A for which there exists λ ε kx such that imageΨd(f(a)) = λΨd(a) for all imagea set membership, variant A. The “standard” similarities are the ones obtained as compositions of automorphisms, antiautomorphisms, and scalar maps of the algebra A.