中文

Dual presentation and linear basis of the Temperley-Lieb algebras

群论 2010-06-03 v3

摘要

The braid group BnB_n maps homomorphically into the Temperley-Lieb algebra \TLn\TL_n. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group BnB_n form a basis for the vector space underlying the Temperley-Lieb algebra \TLn\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.

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}
}