  The BMS symmetry and related near horizon symmetry play important roles in
holography in asymptotically flat spacetimes. They may also be crucial for
solving the information paradox. But we still don't fully understand those
infinite-dimensional symmetries. On the other hand, $W_{1+\infty}$ symmetry is
the quantum version of area-preserving diffeomorphism of a plane. It is a
dynamical symmetry of quantum Hall liquid and can be used to classify the
quantum Hall universality classes. In this paper, we will show that the near
horizon symmetry can be obtained from the $W_{1+\infty}$ symmetry. Based on
this result, the black holes in three dimensional spacetime can be classified
just as in the quantum Hall liquid. It also gives the result that the radius of
black hole are quantized. This gives another evidence that our early claim
"black hole can be considered as a kind of topological insulator" is correct.
