Fibered quadratic Hopf algebras related to Schubert calculus
type: Item
instance of: scholarly article
title: Fibered quadratic Hopf algebras related to Schubert calculus
zbMATH Open document ID: 0962.16028
author: Claudio Procesi
author: Sergey Fomin
published in: Journal of Algebra
publication date: 2001-03-08T00:00:00Z
review text: The paper is concerned with the study of a family of quadratic associative algebras \({\mathcal E}_n\) introduced by \textit{S. Fomin} and \textit{A. N. Kirillov} [Advances in geometry, Prog. Math. 172, 147-182 (1999; Zbl 0940.05070)]. A Hopf algebra structure is defined on the twisted group algebra \({\mathcal E}_n\{{\mathcal S}_n\}\), where \({\mathcal S}_n\) is the symmetric group. This structure is used to prove that \({\mathcal E}_n\) can be decomposed as a graded module into a tensor product, one of the tensor factors being \({\mathcal E}_{n-1}\).
reviewed by: Sorin Dascalescu
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S37
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 1523169
zbMATH Keywords: quadratic algebras
zbMATH Keywords: Hopf algebras
zbMATH Keywords: cohomology of flag manifolds
zbMATH Keywords: twisted group algebras
zbMATH Keywords: graded algebras
zbMATH Keywords: tensor products
MaRDI profile type: Publication
OpenAlex ID: W2088748455
Wikidata QID: Q105613627
cites work: Q3933122
cites work: Q4280747
cites work: Q4227181
cites work: Q4524600
cites work: Q4227189
DOI: 10.1006/JABR.1999.7957
description: scientific article; zbMATH DE number 1523169