turkmath.org

An ordered *-space is a complex vector space endowed with an involution and a strict cone, with certain compatibility conditions. A quantisation of an ordered *-space Z is a sequence of strict cones in M_n(Z), the tensor product of the C*-algebra of n x n complex matrices with Z, with certain compatibility conditions. We show that to any ordered *-space one can associate a weak quantisation (the largest) and strong quantisation (the smallest) and that these have certain universality properties. In the end we comment on some problems in quantisations of topologically ordered *-spaces.