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

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.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 634–641, May, 2004.