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TMF, 1999, Volume 118, Number 2, Pages 205–216 (Mi tmf694)  

This article is cited in 2 scientific papers (total in 2 papers)

Outer automorphisms of $sl(2)$, integrable systems, and mappings

A. V. Tsiganov

St. Petersburg State University, Faculty of Physics

Abstract: Outer automorphisms of infinite-dimensional representations of the Lie algebra $sl(2)$ are used to construct Lax matrices for integrable Hamiltonian systems and discrete integrable mappings. The known results are reproduced, and new integrable systems are constructed. Classical $r$-matrices corresponding to the Lax representation with the spectral parameter are dynamic. This scheme is advantageous because quantum systems naturally arise in the framework of the classical $r$-matrix Lax representation and the corresponding quantum mechanical problem admits a variable separation.

DOI: https://doi.org/10.4213/tmf694

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English version:
Theoretical and Mathematical Physics, 1999, 118:2, 164–172

Bibliographic databases:

Received: 30.06.1998

Citation: A. V. Tsiganov, “Outer automorphisms of $sl(2)$, integrable systems, and mappings”, TMF, 118:2 (1999), 205–216; Theoret. and Math. Phys., 118:2 (1999), 164–172

Citation in format AMSBIB
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\paper Outer automorphisms of $sl(2)$, integrable systems, and mappings
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\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
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\pages 164--172
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Tsiganov, “Canonical transformations of the extended phase space and integrable systems”, Theoret. and Math. Phys., 124:1 (2000), 918–937  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. A. V. Tsiganov, “An integrable system related to the spherical top and the Toda chain”, Theoret. and Math. Phys., 124:2 (2000), 1121–1131  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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