Bilinear forms and (hyper-) determinants
type: Item
instance of: scholarly article
title: Bilinear forms and (hyper-) determinants
zbMATH Open document ID: 0861.18006
author: Giandomenico Boffi
published in: Advances in Mathematics
publication date: 1997-05-12T00:00:00Z
review text: It is the purpose of this paper to describe the homology of \(K_A\) (Koszul complex), in the case \(n=2\). The article is organized as follows. Section 2 contains some preliminaries together with the definition of the complexes \(B(a,b;A)\). Section 3 shows that over \(\mathbb{C}\), the bihomogeneous components of \(K_A\) are expressible in terms of the complexes \(B(a,b;A)\). Section 4 completely describes all \(H_\bullet(B(a,b;A))\), under the assumption that \(A\) is a square and invertible matrix. Section 5 derives from Section 4 a description of \(H_\bullet (K_A)\) over \(\mathbb{C}\), in case \(A\) is invertible, and provides some clues on \(H_\bullet(K_A)\), when \(A\) is not a square invertible matrix.
Mathematics Subject Classification ID: 18G35
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 13D25
Mathematics Subject Classification ID: 15A63
zbMATH DE Number: 949645
zbMATH Keywords: hyperdeterminant
zbMATH Keywords: homology of Koszul complex
zbMATH Keywords: bihomogeneous components
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: aima.1996.0068
OpenAlex ID: W2016183208
DOI: 10.1006/AIMA.1996.0068
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description: scientific article; zbMATH DE number 949645