Dual presentation and linear basis of the Temperley-Lieb algebras
群论
2010-06-03 v3
摘要
The braid group maps homomorphically into the Temperley-Lieb algebra . It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group form a basis for the vector space underlying the Temperley-Lieb algebra . 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.
引用
@article{arxiv.math/0403429,
title = {Dual presentation and linear basis of the Temperley-Lieb algebras},
author = {Eon-Kyung Lee and Sang Jin Lee},
journal= {arXiv preprint arXiv:math/0403429},
year = {2010}
}