Dynamic systems related to the Cremmer–Gervais $R$-matrix

E. V. Damaskinsky; P. P. Kulish; M. Chaichian

E. V. Damaskinsky ; P. P. Kulish ; M. Chaichian

Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 1, pp. 101-112 Citer cet article

E. V. Damaskinsky; P. P. Kulish; M. Chaichian. Dynamic systems related to the Cremmer–Gervais $R$-matrix. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 1, pp. 101-112. http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a2/

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     author = {E. V. Damaskinsky and P. P. Kulish and M. Chaichian},
     title = {Dynamic systems related to the {Cremmer{\textendash}Gervais} $R$-matrix},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {101--112},
     year = {1998},
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     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_1_a2/}
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Résumé

The generalized Cremmer–Gervais $R$-matrix, which is a twist of the standard $sl_q(3)$ $R$-matrix, depends on two additional parameters. We discuss the properties of this $R$-matrix and construct two associated dynamic systems: the $q$-oscillator that is covariant with respect to the corresponding quantum group and an integrable spin chain with a non-Hermitian Hamiltonian.

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