2017
Том 69
№ 6

# Growth of generalized Temperley–Lieb algebras connected with simple graphs

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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