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2006.287: Double-elliptic dynamical systems from generalized Mukai-Sklyanin algebras

2006.287: H. W. Braden, A. Gorsky, A. Odesskii and V. Rubtsov (2002) Double-elliptic dynamical systems from generalized Mukai-Sklyanin algebras. Nuclear Physics B, 633 (3). pp. 414-442. ISSN 0550-3213

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DOI: 10.1016/S0550-3213(02)00248-1

Abstract

We consider the double-elliptic generalisation of dynamical systems of Calogero–Toda–Ruijsenaars type using finite-dimensional Mukai–Sklyanin algebras. The two-body system, which involves an elliptic dependence both on coordinates and momenta, is investigated in detail and the relation with Nambu dynamics is mentioned. We identify the 2D complex manifold associated with the double elliptic system as an elliptically fibered rational ("1/2K3") surface. Some generalisations are suggested which provide the ground for a description of the N-body systems. Possible applications to SUSY gauge theories with adjoint matter in d=6 with two compact dimensions are discussed.

Item Type:Article
Subjects:MSC 2000 > 14 Algebraic geometry
MSC 2000 > 16 Associative rings and algebras
MSC 2000 > 17 Nonassociative rings and algebras
MSC 2000 > 53 Differential geometry
MIMS number:2006.287
Deposited By:Miss Louise Stait
Deposited On:14 August 2006

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