### Abstract

On the coordinate ring of GL_{q}(n), we show that the trace of _{q}X^{m}, the q-analogue of the mth power of Xε{lunate}GL_{q}(n), is represented by the polynomial of tr(_{q}X^{k}), 1≤k≤n-1, and det _{q}X for m≥n by using the quantum Cayley-Hamilton formula. This shows that, if one can take tr(_{q}X^{k}), k=1, 2, ..., as commutative Hamiltonians on the coordinate ring of GL_{q}(n), the number of algebraic independent Hamiltonians is finite. Furthermore we show that the first Hamiltonian tr(_{q}X) and the second Hamiltonian tr(_{q}X^{2}) commute with each other. We observe the q-analogue of the Toda molecule by using quantum group symmetry.

Original language | English |
---|---|

Pages (from-to) | 43-50 |

Number of pages | 8 |

Journal | Physics Letters A |

Volume | 183 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1993 Nov 29 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Algebraic dependence of Hamiltonians on the coordinate ring of the quantum group GL _{q}(n).** / Ikeda, Kaoru.

Research output: Contribution to journal › Article

_{q}(n)',

*Physics Letters A*, vol. 183, no. 1, pp. 43-50. https://doi.org/10.1016/0375-9601(93)90887-6

}

TY - JOUR

T1 - Algebraic dependence of Hamiltonians on the coordinate ring of the quantum group GLq(n)

AU - Ikeda, Kaoru

PY - 1993/11/29

Y1 - 1993/11/29

N2 - On the coordinate ring of GLq(n), we show that the trace of qXm, the q-analogue of the mth power of Xε{lunate}GLq(n), is represented by the polynomial of tr(qXk), 1≤k≤n-1, and det qX for m≥n by using the quantum Cayley-Hamilton formula. This shows that, if one can take tr(qXk), k=1, 2, ..., as commutative Hamiltonians on the coordinate ring of GLq(n), the number of algebraic independent Hamiltonians is finite. Furthermore we show that the first Hamiltonian tr(qX) and the second Hamiltonian tr(qX2) commute with each other. We observe the q-analogue of the Toda molecule by using quantum group symmetry.

AB - On the coordinate ring of GLq(n), we show that the trace of qXm, the q-analogue of the mth power of Xε{lunate}GLq(n), is represented by the polynomial of tr(qXk), 1≤k≤n-1, and det qX for m≥n by using the quantum Cayley-Hamilton formula. This shows that, if one can take tr(qXk), k=1, 2, ..., as commutative Hamiltonians on the coordinate ring of GLq(n), the number of algebraic independent Hamiltonians is finite. Furthermore we show that the first Hamiltonian tr(qX) and the second Hamiltonian tr(qX2) commute with each other. We observe the q-analogue of the Toda molecule by using quantum group symmetry.

UR - http://www.scopus.com/inward/record.url?scp=43949163312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43949163312&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(93)90887-6

DO - 10.1016/0375-9601(93)90887-6

M3 - Article

AN - SCOPUS:43949163312

VL - 183

SP - 43

EP - 50

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 1

ER -