Growth of generalized Temperley–Lieb algebras connected with simple graphs

  • M. V. Zavodovskii
  • Yu. S. Samoilenko Iн-т математики НАН України, Київ

Abstract

We prove that the generalized Temperley–Lieb algebras associated with simple graphs Γ have linear growth if and only if the graph Γ coincides with one of the extended Dynkin graphs \( {\tilde A_n} \), \( {\tilde D_n} \), \( {\tilde E_6} \), or \( {\tilde E_7} \). An algebra \( T{L_{\Gamma, \tau }} \) has exponential growth if and only if the graph Γ coincides with none of the graphs \( {A_n} \), \( {D_n} \), \( {E_n} \), \( {\tilde A_n} \), \( {\tilde D_n} \), \( {\tilde E_6} \), and \( {\tilde E_7} \).
Published
25.11.2009
How to Cite
Zavodovskii, M. V., and Y. S. Samoilenko. “Growth of Generalized Temperley–Lieb Algebras Connected With Simple Graphs”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, no. 11, Nov. 2009, pp. 1579-85, https://umj.imath.kiev.ua/index.php/umj/article/view/3124.
Section
Short communications