Growth of generalized Temperley–Lieb algebras connected with simple graphs - Zavodovskii, M. V.; Samoilenko, Yu. S. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
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 \( A_n \), \( D_n \), \( E_6 \), or \( E_7 \). An algebra \( TL_Γ, τ \) has exponential growth if and only if the graph Γ coincides with none of the graphs \( A_n \), \( D_n \), \( E_n \), \( A_n \), \( D_n \), \( E_6 \), and \( E_7 \).