The properties of the set { L} of extended jordanian twists for algebra sl(3) are studied. Starting from the simplest algebraic construction --- the peripheric Hopf algebra U_ P'(0,1)(sl(3)) --- we construct explicitly the complete family of extended twisted algebras { U_ E(\theta)(sl(3))} corresponding to the set of 4-dimensional Frobenius subalgebras { L(\theta)} in sl(3). It is proved that the extended twisted algebras with different values of the parameter \theta are connected by a special kind of Reshetikhin twist. We study the relations between the family { U_E(\theta)(sl(3))} and the one-dimensional set { U_DJR(\lambda)(sl(3))} produced by the standard Reshetikhin twist from the Drinfeld--Jimbo quantization U_DJ(sl(3)). These sets of deformations are in one-to-one correspondence: each element of { U_E(\theta)(sl(3))} can be obtained by a limiting procedure from the unique point in the set { U_DJR(\lambda)(sl(3))}.
Categories: math.QA