Elliptic algebras

Details Elliptic algebras Elliptic algebras

2003-03-03

arxiv.org/abs/math/0303021v1

Russ.Math.Surveys 57 (2002) 6

Mathematics

Quantum Algebra

Latex, 50 pages, to appear in Russian Math. Surveys 57:6 (2002)

Scientific paper

The survey is devoted to associative $\Z_{\ge0}$-graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). We consider examples of such algebras depending on two continuous parameters (namely, on an elliptic curve and a point on this curve) which 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.

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