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Elliptic algebras | | Alexander Odesskii
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3 Mar 2003 | | Journal: | Russ.Math.Surveys 57 (2002) 6 | | Subject: | Quantum Algebra; Exactly Solvable and Integrable Systems; Algebraic Geometry | math.QA hep-th math.AG nlin.SI | | Abstract: | The survey is devoted to associative $_{ge0}$-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. | | Source: | arXiv, math.QA/0303021 | | Services: | Forum | Review | PDF | Favorites | |
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