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We study some combinatorial and algebraic properties of certain quadraticalgebras related with dynamical classical and classical Yang-Baxter equations.One can find more details about the content of present paper in ExtendedAbstract.

symmetry, integrability and geometry: methods and applications

On Some Quadratic Algebras I $\frac{1}{2}$: Combinatorics of Dunkl and  Gaudin Elements, Schubert, Grothendieck, Fuss-Catalan, Universal Tutte and  Reduced Polynomials