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On a class of skew classical r-matrices with large carrier

Vladimir D. Lyakhovsky
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Abstract

Classical r-matrices with carriers g_c containing the Borel subalgebra b(+,g) of simple Lie algebra g are studied. Using the graphycal presentation of the dual Lie algebra g#(r) we show that such solutions of the CYBE always exist. To obtain the explicit form of these r-matrices we find the dual coordinates in which the adjoint action of g_c can be reduced. This gives us the detailed structure of the Jordanian r-matrices that are the candidates for enlarging the initial full chain r-matrix. We search the desired solution in the factorized form. This leads to the unique transformation: the initial chain is to be substituted by a special kind of peripheric r-matrice. To illustrate the method we consider the case of g=sl(11) in full details.

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Vladimir D. Lyakhovsky. 2004-10-22. On a class of skew classical r-matrices with large carrier. https://arxiv.org/abs/math/0410486

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