Generic \(8\)-dimensional algebras with mixed basis-graph
type: Item
instance of: scholarly article
title: Generic \(8\)-dimensional algebras with mixed basis-graph
zbMATH Open document ID: 0799.16021
author: Thierry Dana-Picard
published in: Pacific Journal of Mathematics
publication date: 1994-11-23T00:00:00Z
review text: Deformation theory is the appropriate tool for describing the irreducible components of the scheme \(\text{Alg}_ n\) which parametrizes the structures of \(n\)-dimensional associative algebras with unit. Each component is ``dominated'' by one generic or quasi-generic algebra or family of algebras (genericity means that the algebra or the family has only trivial infinitesimal deformations, and quasi-genericity means that the algebra or the family has non-trivial infinitesimal deformations, but no algebraic deformation). The components dominated by a generic algebra (or family) are reduced, while the components dominated by a quasi- generic family are non-reduced. The invariants which are used for that classification are the basis-graph, both weighted and unweighted, of an associative algebra. In this paper the 8-dimensional algebras with mixed basis-graph are classified and lower bounds for the numbers of irreducible components of the scheme \(\text{Alg}_ 8\), reduced and non reduced, are given.
reviewed by: Thierry Dana-Picard
Mathematics Subject Classification ID: 16S80
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 597577
zbMATH Keywords: genericity
zbMATH Keywords: irreducible components
zbMATH Keywords: scheme
zbMATH Keywords: \(n\)-dimensional associative algebras
zbMATH Keywords: quasi-generic algebra
zbMATH Keywords: infinitesimal deformations
zbMATH Keywords: quasi- genericity
zbMATH Keywords: invariants
zbMATH Keywords: basis-graph
zbMATH Keywords: 8-dimensional algebras
MaRDI profile type: Publication
full work available at URL: pjm.1994.164.229
OpenAlex ID: W2024259533
DOI: 10.2140/PJM.1994.164.229
description: scientific article; zbMATH DE number 597577