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http://dx.doi.org/10.4134/JKMS.2010.47.3.445

DUAL PRESENTATION AND LINEAR BASIS OF THE TEMPERLEY-LIEB ALGEBRAS  

Lee, Eon-Kyung (DEPARTMENT OF MATHEMATICS SEJONG UNIVERSITY)
Lee, Sang-Jin (DEPARTMENT OF MATHEMATICS KONKUK UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.47, no.3, 2010 , pp. 445-454 More about this Journal
Abstract
The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector space underlying the Temperley-Lieb algebra $TL_n$. 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;
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