### Abstract

We associate a dynamical r-matrix with any such subalgebra ℒ of a finite dimensional self-dual Lie algebra A for which the scalar product of A remains nondegenerate on ℒ and there exists a nonempty open subset ℒ̌ ⊂ ℒ so that the restriction of (ad λ) ∈ End (A) to ℒ^{⊥} is invertible ∀λ ∈ ℒ̌. This r-matrix is also well-defined if ℒ is the grade zero subalgebra of an affine Lie algebra A obtained from a twisted loop algebra based on a finite dimensional self-dual Lie algebra script G sign. Application of evaluation homomorphisms to the twisted loop algebras yields spectral parameter dependent script G sign ⊗ script G sign-valued dynamical r-matrices that are generalizations of Felder's elliptic r-matrices.

Original language | English |
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Pages (from-to) | 1318-1324 |

Number of pages | 7 |

Journal | Czechoslovak Journal of Physics |

Volume | 51 |

Issue number | 12 |

DOIs | |

Publication status | Published - Dec 1 2001 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Czechoslovak Journal of Physics*,

*51*(12), 1318-1324. https://doi.org/10.1023/A:1013317902962