On classical dynamical r-matrices, Lax algebras and integrable gl(n) spin-Calogero models

In the present paper we consider the usage of classical dynamical non-skew-symmetric r-matrices with spectral parameters in the theory of integrable systems. We construct — in complete analogy with non-dynamical case 26, 27 — general position Lax matrices satisfying classical r-matrix Poisson brackets. We consider an example of the Lie algebra gl(n), dynamical r-matrix of Calogero model (equivalent to that of 8) and many-poled Lax matrix with N first order poles. With its help we obtain a new variant of gl(n) multi-spin-Calogero (Gaudin-Calogero) model, integrable without an additional reduction. The N=1 spin-Calogero case is considered in details.