  Recently V.Drinfeld formulated a number of problems in quantum group theory.
In particular, he suggested to consider ``set-theoretical'' solutions of the
quantum Yang-Baxter equation, i.e. solutions given by a permutation $R$ of the
set $X\times X$, where $X$ is a fixed finite set. In this note we study such
solutions, which satisfy the unitarity and the crossing symmetry conditions --
natural conditions arising in physical applications. More specifically, we
consider ``linear'' solutions: the set $X$ is an abelian group, and the map $R$
is an automorphism of $X\times X$. We show that in this case, solutions are in
1-1 correspondence with pairs $a,b\in \End X$, such that $b$ is invertible and
$bab^{-1}=\frac{a}{a+1}$. Later we consider ``affine'' solutions ($R$ is an
automorphism of $X\times X$ as a principal homogeneous space), and show that
they have a similar classification. The fact that these classifications are so
nice leads us to think that there should be some interesting structure hidden
behind this problem.
