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The bubble algebra: structure of a two-colour Temperley–Lieb Algebra

Grimm, Uwe and Martin, Paul P. (2003). The bubble algebra: structure of a two-colour Temperley–Lieb Algebra. Journal of Physics A: Mathematical and General, 36(42) pp. 10551–10571.

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We define new diagram algebras providing a sequence of multiparameter generalizations 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.

Item Type: Journal Item
ISSN: 0305-4470
Extra Information: Preprint version math-ph/0307017 available at
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 2199
Depositing User: Uwe Grimm
Date Deposited: 07 Jun 2006
Last Modified: 08 Dec 2018 06:57
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