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))}.Comment: 14 pages, LaTeX 20