Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series
type: Item
instance of: scholarly article
title: Racah algebras, the centralizer \(Z_n(\mathfrak{sl}_2)\) and its Hilbert-Poincaré series
zbMATH Open document ID: 1504.17017
author: Julien Gaboriaud
author: Luc Vinet
author: N. Crampe
author: L. Poulain d'Andecy
published in: Annales Henri Poincaré
publication date: 2022-06-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/2105.01086
review text: The paper under review shows that a certain quotient \(sR(n)\) of the higher rank Racah algebra \(R(n)\) by a centrally generated ideal is isomorphic to the centralizer of the diagonal embedding of \(U(\mathfrak{sl}_2)\) into \(U(\mathfrak{sl}_2)^{\otimes n}\). This description is used to give a presentation of \(sR(n)\) and to determine the Hilbert-Poincaré series of this algebra. Some extensions and generalizations of these results are discussed.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16S30
Mathematics Subject Classification ID: 81R05
zbMATH DE Number: 7543734
zbMATH Keywords: Racah algebra
zbMATH Keywords: center
zbMATH Keywords: centralizer
zbMATH Keywords: presentation
zbMATH Keywords: Hilbert-Poincaré series
describes a project that uses: OEIS
MaRDI profile type: Publication
OpenAlex ID: W4220943658
arXiv ID: 2105.01086
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DOI: 10.1007/S00023-021-01152-Y
description: scientific article