Abstract
Using a graphic presentation of the dual Lie algebra \(\mathfrak{g}\) # (r) for a simple algebra \(\mathfrak{g}\), it is possible to show that there always exist solutions rech of the classical Yang—Baxter equation with a parabolic carrier. To get a closed-form expression for rech, we find dual coordinates in which the adjoint action of the carrier \(\mathfrak{g}\) c is reducible. This allows us to find the structure of Jordanian r-matrices rJ which are candidates for enlarging the initial full chain rfch and realize the desired solution rech in the factorized form rech ≈ rfch + rJ. We obtain a unique transformation: the canonical chain has to be replaced by a special kind of peripheric r-matrices, rfch → rrfch. To illustrate the method, the case of \(\mathfrak{g}\)=sl(11) is considered in the full detail. Bibliography: 11 titles.
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