  We show that smooth type IIA Killing horizons with compact spatial sections
preserve an even number of supersymmetries, and that the symmetry algebra of
horizons with non-trivial fluxes includes an sl(2,R) subalgebra. This confirms
the conjecture of [1] for type IIA horizons. As an intermediate step in the
proof, we also demonstrate new Lichnerowicz type theorems for spin bundle
connections whose holonomy is contained in a general linear group.
