2017
Том 69
№ 9

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Growth of generalized Temperley–Lieb algebras connected with simple graphs

Samoilenko Yu. S., Zavodovskii M. V.

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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 \( {\tilde E_7} \).

English version (Springer): Ukrainian Mathematical Journal 61 (2009), no. 11, pp 1858-1864.

Citation Example: Samoilenko Yu. S., Zavodovskii M. V. Growth of generalized Temperley–Lieb algebras connected with simple graphs // Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1579-1585.

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