Dual presentation and linear basis of the Temperley-Lieb algebras

Details Dual presentation and linear basis of the Temperley-Lieb algebras Dual presentation and linear basis of the Temperley-Lieb algebras

2004-03-25

arxiv.org/abs/math/0403429v3

Journal of the Korean Mathematical Society, vol. 47, no. 3, pp. 445-454, 2010

Mathematics

Group Theory

Scientific paper

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.

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