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Author Fendley, Paul ♦ Krushkal, Vyacheslav
Source arXiv.org
Content type Text
File Format PDF
Date of Submission 2008-06-20
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics
Subject Keyword Mathematics - Combinatorics ♦ Condensed Matter - Statistical Mechanics ♦ Mathematics - Geometric Topology ♦ Mathematics - Quantum Algebra ♦ math ♦ physics:cond-mat
Abstract We study the connections between link invariants, the chromatic polynomial, geometric representations of models of statistical mechanics, and their common underlying algebraic structure. We establish a relation between several algebras and their associated combinatorial and topological quantities. In particular, we define the chromatic algebra, whose Markov trace is the chromatic polynomial \chi_Q of an associated graph, and we give applications of this new algebraic approach to the combinatorial properties of the chromatic polynomial. In statistical mechanics, this algebra occurs in the low temperature expansion of the Q-state Potts model. We establish a relationship between the chromatic algebra and the SO(3) Birman-Murakami-Wenzl algebra, which is an algebra-level analogue of the correspondence between the SO(3) Kauffman polynomial and the chromatic polynomial.
Description Reference: Adv. Theor. Math. Phys. 14 (2010), 507-540
Educational Use Research
Learning Resource Type Article
Page Count 25


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