## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 36, Number 1 (2007), 73-77.

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

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

#### 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.

#### Article information

**Source**

Hokkaido Math. J., Volume 36, Number 1 (2007), 73-77.

**Dates**

First available in Project Euclid: 29 September 2010

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1285766663

**Digital Object Identifier**

doi:10.14492/hokmj/1285766663

**Mathematical Reviews number (MathSciNet)**

MR2309822

**Zentralblatt MATH identifier**

1130.11018

**Subjects**

Primary: 11E76: Forms of degree higher than two

**Keywords**

symmetric trilinear form automorphism group unique representation sum of powers of linear forms

#### Citation

S{\L}ADEK, Andrzej; WO{\L}OWIEC-MUSIA{\L}, Ma{\l}gorzata. Automorphisms of $\Sigma_{n+1}-$invariant trilinear forms. Hokkaido Math. J. 36 (2007), no. 1, 73--77. doi:10.14492/hokmj/1285766663. https://projecteuclid.org/euclid.hokmj/1285766663