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Growth of generalized Temperley–Lieb algebras connected with simple graphs

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Ukrainian Mathematical Journal Aims and scope

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 \( {\tilde E_7} \).

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kiev, Ukraine

    M. V. Zavodovskii & Yu. S. Samoilenko

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  1. M. V. Zavodovskii
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  2. Yu. S. Samoilenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 61, No. 11, pp. 1579–1584, November, 2009.

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Zavodovskii, M.V., Samoilenko, Y.S. Growth of generalized Temperley–Lieb algebras connected with simple graphs. Ukr Math J 61, 1858–1864 (2009). https://doi.org/10.1007/s11253-010-0318-6

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  • DOI: https://doi.org/10.1007/s11253-010-0318-6

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