### Abstract

The key point of the Hamiltonian formalism of Toda molecules is the commutativity of the Hamiltonians (tr y^{k}, tr y^{l})=0, where y in GL(n) and (,) is a Poisson bracket associated with the classical r-matrix. To quantize the Toda molecule, we have to consider the q-analogue of the above formula. In this paper, we show the commutativity of the quantized first- and higher-order Hamiltonians (tr_{q} X^{m}, tr_{q} X)=0, where X is a matrix of quantum group GL_{q}(n).

Original language | English |
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Article number | 028 |

Pages (from-to) | 5969-5977 |

Number of pages | 9 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 27 |

Issue number | 17 |

DOIs | |

Publication status | Published - 1994 Dec 1 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)