ON QUANTUM ITO ALGEBRAS AND THEIR DECOMPOSITIONS

A simple axiomatic characterization of the noncommutative Ito algebra is given and a pseudo-Euclidean fundamental representation for such al gebra is described. It is proved that every Ito algebra with a quotien t identity has a faithful representation in a Minkowski space and is c anonically decomposed into the orthogonal sum of quantum Brownian (Wie ner) 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 a s it is stated by the Levy-Khinchin Theorem in the classical case. Two basic examples of noncommutative Ito finite group algebras are consid ered.