DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS

Eon-Kyung Lee, Sangjin Lee

Type: Article

Publication Date: 2010-05-01

Citations: 6

DOI: https://doi.org/10.4134/jkms.2010.47.3.445

Abstract

The braid group <TEX>$B_n$</TEX> maps homomorphically into the Temperley-Lieb algebra <TEX>$TL_n$</TEX>. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group <TEX>$B_n$</TEX> form a basis for the vector space underlying the Temperley-Lieb algebra <TEX>$TL_n$</TEX>. 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.

Locations

Journal of the Korean Mathematical Society - View - PDF
arXiv (Cornell University) - View - PDF

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