Growth of generalized Temperley–Lieb algebras connected with simple graphs

• Date: 2009
• Main Authors: Zavodovskii, M. V., Samoilenko, Yu. S., Заводовский, М. В., Самойленко, Ю. С.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3124
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 }}...