Subsystems of an isolated quantum system in finite quantum mechanics

Any Hilbert space with composite dimension can be decomposed into a tensor product of Hilbert spaces of lower dimensions. Such a factorization makes it possible to decompose a quantum system into subsystems. Using a modification of quantum mechanics, in which the continuous unitary group in a Hilbert space is replaced with a permutation representation of a finite group, we suggest a model for the constructive study of decompositions of an isolated quantum system into subsystems. To investigate the behavior of composite systems resulting from decompositions, we develop algorithms based on methods of computer algebra and computational group theory.