DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS

Title & Authors
DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS
Lee, Eon-Kyung; Lee, Sang-Jin;

Abstract
The braid group $\small{B_n}$ maps homomorphically into the Temperley-Lieb algebra $\small{TL_n}$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $\small{B_n}$ form a basis for the vector space underlying the Temperley-Lieb algebra $\small{TL_n}$. In this paper, we establish that there is a dual presentation of Temperley-Lieb algebras that corresponds to the dual presentation of braid groups, and then give a simple geometric proof for Zinno's theorem, using the interpretation of simple elements as non-crossing partitions.
Keywords
Temperley-Lieb algebra;braid group;dual presentation;noncrossing partition;
Language
English
Cited by
1.
Noncrossing partitions, fully commutative elements and bases of the Temperley–Lieb algebra, Journal of Knot Theory and Its Ramifications, 2016, 25, 06, 1650035
2.
Dual braid monoids, Mikado braids and positivity in Hecke algebras, Mathematische Zeitschrift, 2017, 285, 1-2, 215
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