Diagram calculus for a type affine C Temperley-Lieb algebra, II

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Abstract

In a previous paper, we presented an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley-Lieb algebra having a basis indexed by the fully commutative elements of the Coxeter group of type affine C. We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the so-called monomial basis of the Temperley-Lieb algebra of type affine C.

Original languageEnglish (US)
JournalJournal of Pure and Applied Algebra
DOIs
StateAccepted/In press - Jan 1 2018

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Temperley-Lieb Algebra
Calculus
Diagram
Algebra
Coxeter Group
Monomial
Faithful
Correspondence

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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abstract = "In a previous paper, we presented an infinite dimensional associative diagram algebra that satisfies the relations of the generalized Temperley-Lieb algebra having a basis indexed by the fully commutative elements of the Coxeter group of type affine C. We also provided an explicit description of a basis for the diagram algebra. In this paper, we show that the diagrammatic representation is faithful and establish a correspondence between the basis diagrams and the so-called monomial basis of the Temperley-Lieb algebra of type affine C.",
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