  For any (1+1)-dimensional (multicomponent) evolution PDE, we define a
sequence of Lie algebras $F^p$, $p=0,1,2,3,...$, which are responsible for all
Lax pairs and zero-curvature representations (ZCRs) of this PDE.
  In our construction, jets of arbitrary order are allowed. In the case of
lower order jets, the algebras $F^p$ generalize Wahlquist-Estabrook
prolongation algebras.
  To achieve this, we find a normal form for (nonlinear) ZCRs with respect to
the action of the group of gauge transformations. One shows that any ZCR is
locally gauge equivalent to the ZCR arising from a vector field representation
of the algebra $F^p$, where $p$ is the order of jets involved in the $x$-part
of the ZCR.
  More precisely, we define a Lie algebra $F^p$ for each nonnegative integer
$p$ and each point $a$ of the infinite prolongation $E$ of the evolution PDE.
So the full notation for the algebra is $F^p(E,a)$.
  Using these algebras, one obtains a necessary condition for two given
evolution PDEs to be connected by a Backlund transformation.
  In this paper, the algebras $F^p(E,a)$ are computed for some PDEs of KdV
type. In a different paper with G. Manno, we compute $F^p(E,a)$ for
multicomponent Landau-Lifshitz systems of Golubchik and Sokolov. Among the
obtained Lie algebras, one encounters infinite-dimensional algebras of certain
matrix-valued functions on some algebraic curves. Besides, some solvable ideals
and semisimple Lie algebras appear in the description of $F^p(E,a)$.
  Applications to classification of KdV and Krichever-Novikov type equations
with respect to Backlund transformations are also briefly discussed.
