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Dynamicalr-matrices on the affinizations of arbitrary self-dual Lie algebras

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Czechoslovak Journal of Physics Aims and scope

Abstract

We associate a dynamicalr-matrix with any such subalgebraL of a finite dimensional self-dual Lie algebraA for which the scalar product ofA remains nondegenerate onL and there exists a nonempty open subsetĽ ⊂L so that the restriction of (ad λ)εEnd(A) toL \(^ \bot \) is invertible ∨λεĽ. Thisr-matrix is also well-defined ifL is the grade zero subalgebra of an affine Lie algebraA obtained from a twisted loop algebra based on a finite dimensional self-dual Lie algebraG. Application of evaluation homomorphisms to the twisted loop algebras yields spectral parameter dependentG ⊗G-valued dynamicalr-matrices that are generalizations of Felder’s ellipticr-matrices.

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Authors and Affiliations

  1. Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, H-6720, Szeged, Hungary

    L. Fehér & B. G. Pusztai

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  1. L. Fehér
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  2. B. G. Pusztai
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Additional information

This work was supported in part by the Hungarian National Science Fund (OTKA) under T034170.

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Fehér, L., Pusztai, B.G. Dynamicalr-matrices on the affinizations of arbitrary self-dual Lie algebras. Czech J Phys 51, 1318–1324 (2001). https://doi.org/10.1023/A:1013317902962

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  • DOI: https://doi.org/10.1023/A:1013317902962

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