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Parameter-dependent solutions of the classical Yang-Baxter equation on \(sl(n,\mathbb{C})\). (English) Zbl 0860.17012
Summary: For any integers \(n\) and \(m\) \((m\geq 4)\) such that \(n+m\) is odd we exhibit triangular solutions of the classical Yang-Baxter equation on \(\text{sl} ((n+1)(m+2), \mathbb{C})\) parametrized by points of a quotient of complex projective space \(\mathbb{P}^{\lfloor n/2\rfloor} (\mathbb{C})\) by the action of the symmetric group \(\text{Sym}(\lfloor (n+1)/2\rfloor)\) and we prove that no two of these solutions are isomorphic.

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
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