Hokkaido Mathematical Journal

S{\L}ADEK Andrzej, WO{\L}OWIEC-MUSIA{\L} Ma{\l}gorzata,

Automorphisms of $\Sigma_{n+1}-$invariant trilinear forms.

Hokkaido Mathematical Journal, 36 (2007) pp.73-77

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Abstract

Examination of automorphism groups of forms is undertaken by many authors. Sometimes the description of such groups is a difficult task. It turns out that a representation of a form as a sum of powers of linear forms may be very helpful, especially when this representation is unique. We show this in the case of $\Sigma_{n+1}-$invariant symmetric trilinear form $\Theta_n$ considered by Egawa and Suzuki.

MSC(Primary)11E76
MSC(Secondary)
Uncontrolled Keywordssymmetric trilinear form, automorphism group, unique representation, sum of powers of linear forms