Orthogonal idempotents in the descent algebra of \(B_ n\) and applications
type: Item
instance of: scholarly article
title: Orthogonal idempotents in the descent algebra of \(B_ n\) and applications
zbMATH Open document ID: 0793.20004
DOI: 10.1016/0022-4049(92)90153-7
author: Nantel Bergeron
author: F. Bergeron
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: Let \(B_ n\) denote the hyperoctahedral group and \(\Sigma(B_ n)\) be its descent algebra. The authors consider some idempotents \(\rho^ k_ n\), \(1 \leq k \leq n\), in \(\Sigma(B_ n)\) and show that the dimensions of the corresponding right ideals \(\mathbb{Q}[B_ n]\rho^ k_ n\) are the numbers of elements of \(B_ n\) having \(k\) positive cycles, respectively. They also prove that the algebra \(\Lambda\) generated by the classes of elements of \(B_ n\) having equal numbers of descents is commutative. They show that they can define some \(\lambda\) operators in \(\Lambda\) which commute with the Hochschild boundary operators, providing a decomposition for the commutative hyperoctahedral algebra homology.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C30
Mathematics Subject Classification ID: 19A22
zbMATH DE Number: 89565
zbMATH Keywords: orthogonal idempotents
zbMATH Keywords: hyperoctahedral group
zbMATH Keywords: descent algebra
zbMATH Keywords: Hochschild boundary operators
zbMATH Keywords: decomposition
zbMATH Keywords: commutative hyperoctahedral algebra homology
reviewed by: Melih Boral
MaRDI profile type: Publication
full work available at URL: 0022-4049(92)90153-7
OpenAlex ID: W1975352674
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description: scientific article; zbMATH DE number 89565