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TMF, 1997, Volume 110, Number 2, Pages 214–227 (Mi tmf962)  

This article is cited in 3 scientific papers (total in 3 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.

DOI: https://doi.org/10.4213/tmf962

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English version:
Theoretical and Mathematical Physics, 1997, 110:2, 168–178

Bibliographic databases:

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

Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
\yr 1997
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\issue 2
\pages 168--178
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    This publication is cited in the following articles:
    1. Tarasov, VE, “Quantization of non-Hamiltonian and dissipative systems”, Physics Letters A, 288:3–4 (2001), 173  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Tarasov, VE, “Phase-space metric for non-Hamiltonian systems”, Journal of Physics A-Mathematical and General, 38:10 (2005), 2145  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    3. Tarasov, VE, “Fractional systems and fractional Bogoliubov hierarchy equations”, Physical Review E, 71:1 (2005), 011102  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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