Representations of Clifford algebras of binary and ternary cubic forms
type: Item
instance of: scholarly article
title: Representations of Clifford algebras of binary and ternary cubic forms
zbMATH Open document ID: 0977.15015
DOI: 10.1007/BF03042379
author: Yamna El Makkab
published in: Advances in Applied Clifford Algebras
publication date: 2002-01-21T00:00:00Z
review text: \textit{D. E. Haile} [Am. J. Math. 106, 1269-1280 (1984; Zbl 0585.13001)], \textit{Ph. Revoy} [Commun. Algebra 11, 1877-1891 (1983; Zbl 0526.15019)] and \textit{Ph. Revoy} and \textit{S. Tesser} [C.R. Acad. Sci., Paris, Sér. I. 318, No. 6, 509-514 (1994; Zbl 0818.11021)] have studied binary and ternary cubic forms which generalize Clifford algebras generated by quadratic forms. Clifford algebras of polynomial forms of degree \(d>2\) were introduced by N. Roby. In this article the author considers special binary cubic forms such as \(f=xy(x+y)\) and \(f=xy^2\). He describes explicitly a corresponding irreducible family of representations in the matrix algebra \(M_3(K)\) \((K\) is a base field) which only depend on one parameter. Associated Weierstrass functions help to represent the results in case of \(K=\mathbb{C}\). It is shown in a direct way that the number of 3D-representations of a cubic form is finite and different from zero.
Mathematics Subject Classification ID: 15A66
zbMATH DE Number: 1502070
zbMATH Keywords: Clifford algebras
zbMATH Keywords: binary cubic forms
zbMATH Keywords: ternary cubic forms
zbMATH Keywords: Weierstrass functions
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf03042379
OpenAlex ID: W1972367538
description: scientific article; zbMATH DE number 1502070