  The Lie algebra of pseudodifferential symbols on the circle has a nontrivial
central extension (by the ``logarithmic'' 2-cocycle) generalizing the Virasoro
algebra. The corresponding extended subalgebra of integral operators generates
the Lie group of classical symbols of all real (or complex) degrees. It turns
out that this group has a natural Poisson-Lie structure whose restriction to
differential operators of an arbitrary integer order coincides with the second
Adler-Gelfand-Dickey structure. Moreover, for any real (or complex) \alpha
there exists a hierarchy of completely integrable equations on the degree
\alpha pseudodifferential symbols, and this hierarchy for \alpha=1 coincides
with the KP one, and for an integer \alpha=n>1$ and purely differential symbol
gives the n-KdV-hierarchy.
