We consider rr-matrix
realization of the quantum deformations of the loop algebras
\tilde{\mathfrak{g}}𝔤̃
corresponding to non-exceptional affine Lie algebras of type
\widehat{\mathfrak{g}}=A^{(1)}_{N-1}𝔤̂=AN−1(1),
B^{(1)}_nBn(1),
C^{(1)}_nCn(1),
D^{(1)}_nDn(1),
A^{(2)}_{N-1}AN−1(2).
For each U_q(\tilde{\mathfrak{g}})Uq(𝔤̃)
we investigate the commutation relations between Gauss coordinates of
the fundamental \mathbb{L}𝕃-operators
using embedding of the smaller algebra into bigger one. The new
realization of these algebras in terms of the currents is given. The
relations between all off-diagonal Gauss coordinates and certain
projections from the ordered products of the currents are presented.
These relations are important in applications to the quantum integrable
models.