Projective resolutions of straightening closed algebras generated by minors
type: Item
instance of: scholarly article
title: Projective resolutions of straightening closed algebras generated by minors
zbMATH Open document ID: 0824.13012
author: Rosa Q. Huang
author: E. L. Green
published in: Advances in Mathematics
publication date: 1995-11-09T00:00:00Z
review text: The authors define a class of algebras called straightening closed algebras, generalizing the algebras generated by minors in a generic matrix. Gröbner bases for the defining ideals of these algebras (viewed as factor rings of free associative \(k\)-algebras, \(k\) a field) are calculated. These are used to get projective resolutions of \(k\), using a construction of Anick. The authors note that, if the Gröbner basis consists of elements of degree two, then the algebra is a Koszul algebra, i.e. \((\text{Tor}_i(k,k))_j=0\) if \(i\neq j\). In fact the setting is more general, factor rings of so called path algebras instead of free associative algebras are allowed.
Mathematics Subject Classification ID: 13F50
Mathematics Subject Classification ID: 13P10
Mathematics Subject Classification ID: 13C40
zbMATH DE Number: 745286
zbMATH Keywords: straightening closed algebras
zbMATH Keywords: projective resolutions
zbMATH Keywords: Gröbner basis
zbMATH Keywords: Koszul algebra
MaRDI profile type: Publication
full work available at URL: aima.1995.1013
OpenAlex ID: W2005271489
DOI: 10.1006/AIMA.1995.1013
description: scientific article; zbMATH DE number 745286