2019
Том 71
№ 11

# Zavodovskii M. V.

Articles: 2
Brief Communications (Russian)

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

Ukr. Mat. Zh. - 2009. - 61, № 11. - pp. 1579-1585

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 ${\tilde E_7}$.

Article (Russian)

### On algebras of the Temperley-Lieb type associated with algebras generated by generators with given spectrum

Ukr. Mat. Zh. - 2004. - 56, № 5. - pp. 634–641

We introduce and study algebras of the Temperley-Lieb type associated with algebras generated by linearly connected generators with given spectrum. We study their representations and the sets of parameters for which representations of these algebras exist.