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This article is cited in 6 scientific papers (total in 6 papers)
Quantum dissipative systems. IV. Analog of Lie algebra and Lie group
V. E. Tarasov Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
Abstract:
The requirement of consistent quantum description of dissipative systems leads to necessity to go beyond Lie algebra and group. In order to describe dissipative (non-Hamiltonian) systems in quantum theory we need to use non-Lie algebra (algebras for which the Jacoby identity is not satisfied) and analytic quasigroups (nonassociative generalization of analytic groups). We prove that this analog is a commutant Lie algebra (an algebra, the commutant of which is a Lie subalgebra) and a commutant associative loop (a loop, commutators of which form an associative subloop (group)). We prove that the tangent algebra of an analytic commutant associative loop (Valya loop) is a commutant Lie algebra (Valya algebra). Examples of commutant Lie algebras are considered.
Received: 30.04.1996
Citation:
V. E. Tarasov, “Quantum dissipative systems. IV. Analog of Lie algebra and Lie group”, TMF, 110:2 (1997), 214–227; Theoret. and Math. Phys., 110:2 (1997), 168–178
Linking options:
https://www.mathnet.ru/eng/tmf962https://doi.org/10.4213/tmf962 https://www.mathnet.ru/eng/tmf/v110/i2/p214
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