On a class of skew classical r-matrices with large carrier
نویسنده
چکیده
The classical r-matrices with carriers gc containing the Borel subalgebra b(g) of simple Lie algebra g are studied. Using the graphical presentation of the dual Lie algebra g(r) we show that such solutions rech of the CYBE always exist. To obtain the explicit form of rech we find the dual coordinates in which the adjoint action of gc can be reduced. This gives us the detailed structure of the Jordanian r-matrices rJ that are the candidates for enlarging the initial full chain rfch. We search the desired solution rech in the factorized form rech ≈ rfch+rJ . This leads to the unique transformation: the canonical chain is to be substituted with a special kind of peripheric r-matrices: rfch −→ rrfch. To illustrate the method the case of g = sl(11) is considered in full details.
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