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2006.286: Elliptic algebras

2006.286: A. V. Odesskii (2002) Elliptic algebras. Russian Mathematical Surveys, 57 (6). pp. 1127-1162. ISSN 1468-4829

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DOI: 10.1070/RM2002v057n06ABEH000573


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 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:2006.286
Deposited By:Miss Louise Stait
Deposited On:14 August 2006

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