Abstract
In [EGAWA, Y.—SUZUKI, H.: Automorphism groups of Σn+1-invariant trilinear forms, Hokkaido Math. J. 11, (1985), 39–47] are explored Σn+1-invariant symmetric trilinear forms and their automorphisms. In the paper we generalize their results to d-linear symmetric forms for any d ≥ 3.
[1] CHLEBOWICZ, A.— SŁADEK, A.— WOŁOWIEC-MUSIAŁ, M.: Automorphisms of certain forms of higher degree over ordered fields, Linear Algebra Appl. 331 (2001), 145–153. http://dx.doi.org/10.1016/S0024-3795(01)00272-510.1016/S0024-3795(01)00272-5Search in Google Scholar
[2] CHLEBOWICZ, A.— WOŁOWIEC-MUSIAŁ, M.: Forms with a unique representation as a sum of powers of linear forms, Tatra Mt. Math. Publ. 32 (2005), 33–39. Search in Google Scholar
[3] EGAWA, Y.— SUZUKI, H.: Automorphism groups of Σn+1-invariant trilinear forms, Hokkaido Math. J. 11, (1985), 39–47. 10.14492/hokmj/1381757688Search in Google Scholar
[4] IARROBINO, A.— KANEV, V.: Power Sums, Gorenstein Algebras, and Determinantal Loci. Lecture Notes in Math. 1721, Springer-Verlag, Berlin-Heidelberg, 1999. Search in Google Scholar
[5] REZNICK, B.: Sums of even powers of real linear forms, Mem. Amer. Math. Soc. 96 (1992), no. 463. Search in Google Scholar
[6] SCHINZEL, A.: Reducibility of a special symmetric form, Acta Math. Inform. Univ. Ostraviensis 14 (2006), 71–74. Search in Google Scholar
[7] SŁADEK, A.— WOŁOWIEC-MUSIAŁ, M.: Automorphism groups of Σn+1-invariant trilinear forms, Hokkaido Math. J. 36 (2007), 73–77. Search in Google Scholar
[8] SMITH, L.: Polynomial Invariants of Finite Groups. Res. Notes Math. 6, Wellesley, Massachusetts, 1995. 10.1201/9781439864470Search in Google Scholar
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