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 |
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ASJC Scopus subject areas
- Algebra and Number Theory
Cite this
Diagram calculus for a type affine C Temperley-Lieb algebra, II. / Ernst, Dana C.
In: Journal of Pure and Applied Algebra, 01.01.2018.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
AN - SCOPUS:85041942327
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
ER -