  Three-dimensional Einstein gravity with negative cosmological constant admits
stationary black holes that are not necessarily spherically symmetric. We
propose boundary conditions for the near horizon region of these black holes
that lead to a surprisingly simple near horizon symmetry algebra consisting of
two affine u(1) current algebras. The symmetry algebra is essentially
equivalent to the Heisenberg algebra. The associated charges give a specific
example of "soft hair" on the horizon, as defined by Hawking, Perry and
Strominger. We show that soft hair does not contribute to the
Bekenstein-Hawking entropy of Banados-Teitelboim-Zanelli black holes and "black
flower" generalizations. From the near horizon perspective the conformal
generators at asymptotic infinity appear as composite operators, which we
interpret in the spirit of black hole complementarity. Another remarkable
feature of our boundary conditions is that they are singled out by requiring
that the whole spectrum is compatible with regularity at the horizon,
regardless the value of the global charges like mass or angular momentum.
Finally, we address black hole microstates and generalizations to cosmological
horizons.
