×

Automorphism and similarity groups of forms determined by the characteristic polynomial. (English) Zbl 0935.11014

Let \(K\) be a field and let \(A\) be a finite-dimensional, commutative, étale algebra over \(K\), where \(\text{char }K= 0\) or \(\text{char }K> n!\), where \(n \geq 3\) is the degree of \(A\) over \(K\). The coefficients of the generic characteristic polynomial \(\chi_A\) determine the norm form \(N_A\) of degree \(n\), the trace forms \(\text{Tr}_A^d\) of degree \(d \geq 3\) (where \(d < \text{char } K\) if \(\text{char }K > 0\)), and the so-called intermediate forms \(M_{A,t}\) of degree \(t\), \(2 \leq t \leq n-1\). The principal results of this paper are complete descriptions of the similarity groups and automorphism groups for the norm, trace, and intermediate forms.

MSC:

11E76 Forms of degree higher than two
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1080/00927878808823631 · Zbl 0645.10022 · doi:10.1080/00927878808823631
[2] DOI: 10.1016/0021-8693(84)90056-5 · Zbl 0536.17010 · doi:10.1016/0021-8693(84)90056-5
[3] DOI: 10.1006/jabr.1994.1265 · Zbl 0813.11024 · doi:10.1006/jabr.1994.1265
[4] DOI: 10.1016/0024-3795(94)00363-7 · Zbl 0867.16010 · doi:10.1016/0024-3795(94)00363-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.