  The microscopic and the macroscopic properties of A-superstatistics, related
to the class A(0,n-1)\equiv sl(1|n) of simple Lie superalgebras are
investigated. The algebra sl(1|n) is described in terms of generators f_1^\pm,
>..., f_n^\pm, which satisfy certain triple relations and are called Jacobson
generators. The Fock spaces of A-superstatistics are investigated and the Pauli
principle of the corresponding statistics is formulated. Some thermal
properties of A-superstatistics are constructed under the assumption that the
particles interact only via statistical interaction imposed by the Pauli
principle. The grand partition function and the average number of particles are
written down explicitly in the general case and in two particular examples: 1)
the particles have one and the same energy and chemical potential; 2) the
energy spectrum of the orbitals is equidistant.
