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Quantum dissipative systems. III. Definition and algebraic structure
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 1, pp. 73-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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Starting from the requirement of a consistent quantum description of dissipative (non-Hamiltonian) systems, which is formulated as the absence of a contradiction between the evolution equations for quantum dissipative systems and quantum commutation relations, we show that the Jacobi identity is not satisfied. Thus, the requirement for a consistent quantum description forces one go beyond the Lie algebra. As a result, anticommutative non-Lie algebras are necessary to describe dissipative (non-Hamiltonian) systems in quantum theory. 
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V. E. Tarasov. Quantum dissipative systems. III. Definition and algebraic structure. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 1, pp. 73-85. http://geodesic.mathdoc.fr/item/TMF_1997_110_1_a5/

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