On the structure of the blob algebra
type: Item
instance of: scholarly article
title: On the structure of the blob algebra
zbMATH Open document ID: 0947.16006
author: Paul Martin
author: David J. Woodcock
published in: Journal of Algebra
publication date: 2000-10-29T00:00:00Z
review text: The aim of this paper is to understand the structure of the standard modules for the two-parameter blob algebra, \(b_n(q,q')\), an algebra arising from the context of transfer matrix algebras in statistical mechanics. Working over a field of characteristic zero, the authors are able to determine the structure of the standard modules for the algebra quite explicitly, obtaining precise results on homomorphisms between standard modules, the blocks of the algebra and the filtration into simple modules of various standard modules. The techniques used involve homological algebra and the calculus of diagrams for \(b_n(q,q')\). The results provide further evidence for a connection with category \(\mathcal O\) for \(\widehat{sl}_2\).
Mathematics Subject Classification ID: 16G30
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16W35
zbMATH DE Number: 1429479
zbMATH Keywords: Temperley-Lieb algebras
zbMATH Keywords: quasi-hereditary algebras
zbMATH Keywords: standard modules
zbMATH Keywords: blob algebras
zbMATH Keywords: transfer matrix algebras
zbMATH Keywords: blocks
zbMATH Keywords: filtrations
zbMATH Keywords: simple modules
reviewed by: R. M. Green
MaRDI profile type: Publication
full work available at URL: jabr.1999.7948
OpenAlex ID: W2037662791
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DOI: 10.1006/JABR.1999.7948
description: scientific article; zbMATH DE number 1429479