ar X iv : m at h - ph / 9 80 70 18 v 1 1 7 Ju l 1 99 8 Volume preserving multidimensional integrable systems and Nambu - Poisson Geometry

ar X iv : m at h / 99 02 12 8 v 2 [ m at h . D G ] 7 M ar 1 99 9 Remarks on Nambu - Poisson , and Nambu - Jacobi brackets

We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get an (n − 1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.

ar X iv : h ep - l at / 9 80 70 28 v 1 1 1 Ju l 1 99 8 COURSE INTRODUCTION TO LATTICE QCD

ar X iv : m at h / 99 07 16 9 v 1 [ m at h . Q A ] 2 6 Ju l 1 99 9 Integrable deformations of Hamiltonian systems and q - symmetries 1

The complete integrability of the hyperbolic Gaudin Hamiltonian and other related integrable systems is shown to be easily derived by taking into account their sl(2, R) coalgebra symmetry. By using the properties induced by such a coalgebra structure, it can be proven that the introduction of any quantum deformation of the sl(2, R) algebra will provide an integrable deformation for such systems...

ar X iv : h ep - t h / 95 07 12 5 v 1 2 4 Ju l 1 99 5 Aspects of Classical and Quantum Nambu Mechanics

We present recent developments in the theory of Nambu mechanics, which include new examples of Nambu-Poisson manifolds with linear Nambu brackets and new representations of Nambu-Heisenberg commutation relations. Mathematics Subject Classification (1991) 70H99, 58F07

Volume Preserving Multidimensional Integrable Systems and Nambu–Poisson Geometry

In this paper we study generalized classes of volume preserving multidimensional integrable systems via Nambu–Poisson mechanics. These integrable systems belong to the same class of dispersionless KP type equation. Hence they bear a close resemblance to the self dual Einstein equation. All these dispersionless KP and dToda type equations can be studied via twistor geometry, by using the method ...