  Topological states of matter are characterized by topological invariant,
which are physical quantities whose values are quantized and do not depend on
details of the measured system. Of these, the easiest to probe in experiments
is the electrical Hall conductance, which is expressed in units of $e^2/h$ ($e$
the electron charge, $h$ the Planck's constant). In the fractional quantum Hall
effect (FQHE), fractional quantized values of the electrical Hall conductance
attest to topologically ordered states, which are states that carry quasi
particles with fractional charge and anyonic statistics. Another topological
invariant, which is much harder to measure, is the thermal Hall conductance,
expressed in units of $\kappa_0T=(\pi^2kB^2/3h)T$ ($kB$ the Boltzmann constant,
$T$ the temperature). For the quantized thermal Hall conductance, a fractional
value attests that the probed state of matter is non-abelian. Quasi particles
in non-abelian states lead to a ground state degeneracy and perform topological
unitary transformations among ground states when braided. As such, they may be
useful for topological quantum computation. In this paper, we report our
measurements of the thermal Hall conductance for several quantum Hall states in
the first excited Landau level. Remarkably, we find the thermal Hall
conductance of the $\nu=5/2$ state to be fractional, and to equal
$2.5\kappa_0T$
