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
ZavodovskiiM. V., and SamoilenkoY. S. “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