Matrix computations in linear superalgebra
type: Item
instance of: scholarly article
title: Matrix computations in linear superalgebra
zbMATH Open document ID: 0672.58006
DOI: 10.1016/0024-3795(88)90057-2
author: O. A. Sánchez-Valenzuela
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Besides an extensive review of many notions under the general framework of linear superalgebra (e.g. supervector spaces, superalgebras, supermodules etc.), the author devotes a good part of the paper to finite dimensional free supermodules over supercommutative superalgebras and the functorial correspondence between free supermodule morphisms and matrices with coefficients in the corresponding supercommutative superalgebra. The discussed functoriality requires a slight modification of the usual matrix multiplication, but it has the advantage of making the analogues of the nongraded formulas to retain their familiar form. The paper can profitably be used, among other things, and as a reference basis for the author's work on supermanifolds and supervector bundles.
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 17A70
zbMATH DE Number: 4100210
zbMATH Keywords: linear superalgebra
zbMATH Keywords: supervector spaces
zbMATH Keywords: superalgebras
zbMATH Keywords: supermodules
reviewed by: E. Vassiliou
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90057-2
OpenAlex ID: W1988293434
cites work: Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
cites work: Q4130629
cites work: INTRODUCTION TO THE THEORY OF SUPERMANIFOLDS
cites work: Q5343374
cites work: Q3222836
cites work: Linear Supergroup Actions. I: On the Defining Properties
description: scientific article; zbMATH DE number 4100210