Cayley's hyperdeterminant: A combinatorial approach via representation theory
type: Item
instance of: scholarly article
title: Cayley's hyperdeterminant: A combinatorial approach via representation theory
zbMATH Open document ID: 1270.15016
author: Mikelis G. Bickis
author: Mohsen Soltanifar
author: Murray R. Bremner
published in: Linear Algebra and its Applications
publication date: 2012-05-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1106.5068
reviewed by: Maria Chiara Brambilla
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 62H17
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 13A50
zbMATH DE Number: 6034517
zbMATH Keywords: multidimensional matrices
zbMATH Keywords: polynomial invariants
zbMATH Keywords: representation theory
zbMATH Keywords: Cayley hyperdeterminant
MaRDI profile type: Publication
OpenAlex ID: W1974126243
arXiv ID: 1106.5068
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DOI: 10.1016/J.LAA.2012.01.037
review text: In 1845, Cayley introduced the concept of hyperdeterminant of a multidimensional matrix. In the case of \(2\times2\times2\) matrices, the hyperdeterminant is a homogeneous polynomial of degree 4 in the 8 entries of the matrix, called Cayley hyperdeterminant.NEWLINENEWLINEIt is well-known that the Cayley hyperdeterminant is invariant under the natural action of \(\mathrm{SL}_2(\mathbb{C})\times \mathrm{SL}_2(\mathbb{C})\times \mathrm{SL}_2(\mathbb{C})\) on \(\mathbb{C}^2\otimes \mathbb{C}^2\otimes \mathbb{C}^2\) and moreover, it generates all the invariant polynomials. In this paper, the authors gives a new proof of this fact, based on a combinatorical approach.
description: scientific article; zbMATH DE number 6034517