Elliptic algebras

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
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/491

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