  A simple axiomatic characterization of the noncommutative Ito algebra is
given and a pseudo-Euclidean fundamental representation for such algebra is
described. It is proved that every quotient Ito algebra has a faithful
representation in a Minkowski space and is canonically decomposed into the
orthogonal sum of quantum Brownian (Wiener) algebra and quantum Levy (Poisson)
algebra. In particular, every quantum thermal noise of a finite number of
degrees of freedom is the orthogonal sum of a quantum Wiener noise and a
quantum Poisson noise as it is stated by the Levy-Khinchin theorem in the
classical case. Two basic examples of non-commutative Ito finite group algebras
are considered.
