### 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 language | English (US) |
---|---|

Journal | Journal of Pure and Applied Algebra |

DOIs | |

State | Accepted/In press - Jan 1 2018 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Diagram calculus for a type affine C Temperley-Lieb algebra, II.** / Ernst, Dana C.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Diagram calculus for a type affine C Temperley-Lieb algebra, II

AU - Ernst, Dana C

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85041942327&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85041942327&partnerID=8YFLogxK

U2 - 10.1016/j.jpaa.2018.02.008

DO - 10.1016/j.jpaa.2018.02.008

M3 - Article

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

SN - 0022-4049

ER -