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In order to describe non-Hamiltonian (dissipative) systems in quantum theory we need to use non-Lie algebra and analytic quasigroup (loop).\n  The author derives that analog of Lie algebra for quantum non-Hamiltonian systems is commutant Lie algebra and analog of Lie group for these systems is analytic commutant associative loop (Valya loop). A commutant Lie algebra is an algebra such that commutant (a subspace which is generated by all commutators) is a Lie subalgebra. 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