### Abstract

It is well known that a classical dynamical r-matrix can be associated with every finite-dimensional self-dual Lie algebra Script G sign by the definition R(ω) := f(ad ω), where ω ∈ Script G sign and f is the holomorphic function given by f(z) = 1/2 coth(z/2) -1 /z for z ∈ ℂ \ 2πiℤ*. We present a new, direct proof of the statement that this canonical r-matrix satisfies the modified classical dynamical Yang-Baxter equation on Script G sign.

Original language | English |
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Pages (from-to) | 10949-10962 |

Number of pages | 14 |

Journal | Journal of Physics A: Mathematical and General |

Volume | 34 |

Issue number | 49 |

DOIs | |

Publication status | Published - Dec 14 2001 |

### ASJC Scopus subject areas

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

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## Cite this

Pusztai, B. G., & Fehér, L. (2001). A note on a canonical dynamical r-matrix.

*Journal of Physics A: Mathematical and General*,*34*(49), 10949-10962. https://doi.org/10.1088/0305-4470/34/49/314