@article{Zavodovskii_Samoilenko_2009, title={Growth of generalized Temperley–Lieb algebras connected with simple graphs}, volume={61}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3124}, abstractNote={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 <span class="InlineEquation" id="IEq1">\( {\tilde A_n} \)</span>, <span class="InlineEquation" id="IEq2">\( {\tilde D_n} \)</span>, <span class="InlineEquation" id="IEq3">\( {\tilde E_6} \)</span>, or <span class="InlineEquation" id="IEq4">\( {\tilde E_7} \)</span>. An algebra <span class="InlineEquation" id="IEq5">\( T{L_{\Gamma, \tau } \)</span> has exponential growth if and only if the graph Γ coincides with none of the graphs <span class="InlineEquation" id="IEq6">\( {A_n} \)</span>, <span class="InlineEquation" id="IEq7">\( {D_n} \)</span>, <span class="InlineEquation" id="IEq8">\( {E_n} \)</span>, <span class="InlineEquation" id="IEq9">\( {\tilde A_n} \)</span>, <span class="InlineEquation" id="IEq10">\( {\tilde D_n} \)</span>, <span class="InlineEquation" id="IEq11">\( {\tilde E_6} \)</span>, and <span class="InlineEquation" id="IEq12">\( {\tilde E_7} \)</span&gt;.}, number={11}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Zavodovskii, M. V. and Samoilenko, Yu. S.}, year={2009}, month={Nov.}, pages={1579-1585} }