In this note we define and compute the Temperley-Lieb algebras associated to the Coxeter-Dynkin graphs of type D_n. The computation relates these algebras to those corresponding to the root systems of type A and B. We also show the connection to braid theory and to the Kauffman bracket and describe a related graphical calculus.
%0 Journal Article
%1 tomDieck1998a
%A tom Dieck, Tammo
%D 1998
%J Arch. Math. (Basel)
%K algebra hecke representation-theory temperley-lieb
%N 5
%P 407--416
%R 10.1007/s000130050284
%T Temperley-Lieb algebras associated to the root system D
%U http://dx.doi.org/10.1007/s000130050284
%V 71
%X In this note we define and compute the Temperley-Lieb algebras associated to the Coxeter-Dynkin graphs of type D_n. The computation relates these algebras to those corresponding to the root systems of type A and B. We also show the connection to braid theory and to the Kauffman bracket and describe a related graphical calculus.
@article{tomDieck1998a,
abstract = {In this note we define and compute the Temperley-Lieb algebras associated to the Coxeter-Dynkin graphs of type D_n. The computation relates these algebras to those corresponding to the root systems of type A and B. We also show the connection to braid theory and to the Kauffman bracket and describe a related graphical calculus.},
added-at = {2009-05-07T14:56:08.000+0200},
author = {tom Dieck, Tammo},
biburl = {https://www.bibsonomy.org/bibtex/208d369c3c688abfa0a28c37b09d7c0d2/njj},
coden = {ACVMAL},
doi = {10.1007/s000130050284},
fjournal = {Archiv der Mathematik},
interhash = {4b5dd484a17aa5dd931b6d8ffb116447},
intrahash = {08d369c3c688abfa0a28c37b09d7c0d2},
issn = {0003-889X},
journal = {Arch. Math. (Basel)},
keywords = {algebra hecke representation-theory temperley-lieb},
mrclass = {57M25 (20F36)},
mrkey = {1649348},
number = 5,
pages = {407--416},
timestamp = {2009-05-07T14:56:08.000+0200},
title = {Temperley-Lieb algebras associated to the root system D},
url = {http://dx.doi.org/10.1007/s000130050284 },
volume = 71,
year = 1998
}