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RATIONAL SOLUTIONS OF THE CYBE AND LOCALLY TRANSITIVE ACTIONS ON ISOTROPIC GRASSMANNIANS

IULIA I. POP

Department of Mathematics, Göteborg University, 41296 Göteborg, Sweden

https://doi.org/10.1142/S0219498805001162Cited by:0 (Source: Crossref)

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 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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