Odesskii, A. V.
(2002)
*Elliptic algebras.*
Russian Mathematical Surveys, 57 (6).
pp. 1127-1162.
ISSN 1468-4829

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## Abstract

This survey is devoted to associative -graded algebras presented by n generators and quadratic relations and satisfying the so-called Poincaré–Birkhoff–Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations.

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: | http://eprints.maths.manchester.ac.uk/id/eprint/491 |

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