Braden, H. W. and Gorsky, A. and Odesskii, A. and Rubtsov, V.
(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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## 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 |
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Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 17 Nonassociative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 53 Differential geometry |

Depositing User: | Ms Lucy van Russelt |

Date Deposited: | 14 Aug 2006 |

Last Modified: | 20 Oct 2017 14:12 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/493 |

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