Geodesic
Outer automorphisms of $sl(2)$, integrable systems, and mappings
Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 205-216

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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. 
@article{TMF_1999_118_2_a2,
     author = {A. V. Tsiganov},
     title = {Outer automorphisms of $sl(2)$, integrable systems, and mappings},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {205--216},
     publisher = {mathdoc},
     volume = {118},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a2/}
}
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A. V. Tsiganov. Outer automorphisms of $sl(2)$, integrable systems, and mappings. Teoretičeskaâ i matematičeskaâ fizika, Tome 118 (1999) no. 2, pp. 205-216. http://geodesic.mathdoc.fr/item/TMF_1999_118_2_a2/