Abstract
This paper continues the investigation of the theory of rational solutions of the CYBE for o(n) from the point of view of orders in the corresponding loop algebra, as it was developed in [8]. As suggested by [8], in the case of "singular vertices", we use the list of connected irreducible subgroups of SO(n) locally transitive on the Grassmann manifolds [Formula: see text] of isotropic k-dimensional subspaces in ℂn obtained in [11]. New arguments based on the analysis of the structure of the stationary subalgebra of a generic point allow us to construct several rational solutions in o(7), o(8) and o(12).
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