2019
Том 71
№ 9

All Issues

Zavodovskii M. V.

Articles: 2
Brief Communications (Russian)

Growth of generalized Temperley–Lieb algebras connected with simple graphs

Samoilenko Yu. S., Zavodovskii M. V.

↓ Abstract   |   Full text (.pdf)

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

Zavodovskii M. V.

↓ Abstract   |   Full text (.pdf)

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.