The Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra

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dc.creatorGrimm, Uwe
dc.creatorMartin, Paul P.
dc.date2003-07-08
dc.date2003-10-09
dc.date.accessioned2026-07-07T10:50:37Z
dc.date.available2026-07-07T10:50:37Z
dc.descriptionWe define new diagram algebras providing a sequence of multiparameter generalisations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional Statistical Mechanics. These algebras give a rigorous foundation to the various "multi-colour algebras" of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in Statistical Mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations.
dc.description24 pages, LaTeX using IOP styles, many figures included; typo in formula (7) corrected
dc.identifierhttps://arxiv.org/abs/math-ph/0307017
dc.identifierhttp://arxiv.org/abs/math-ph/0307017
dc.identifierJ.Phys.A36:10551-10572,2003
dc.identifierdoi:10.1088/0305-4470/36/42/010
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184588
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectRings and Algebras
dc.subject81R12; 82B20; 82B23
dc.titleThe Bubble Algebra: Structure of a Two-Colour Temperley-Lieb Algebra
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