Generalized classical Yang-Baxter equation and regular decompositions
Generalized classical Yang-Baxter equation and regular decompositions
The focus of the paper is on constructing new solutions of the generalized classical Yang-Baxter equation (GCYBE) that are not skew-symmetric. Using regular decompositions of finite-dimensional simple Lie algebras, we construct Lie algebra decompositions of $\mathfrak{g}(\!(x)\!) \times \mathfrak{g}[x]/x^m \mathfrak{g}[x]$. The latter decompositions are in bijection with the solutions to the …