Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-02-21
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Numeration of the formulas is corrected
Scientific paper
10.1088/1751-8113/42/9/095201
Quantum deformations of the structure constants for a class of associative noncommutative algebras are studied. It is shown that these deformations are governed by the quantum central systems which has a geometrical meaning of vanishing Riemann curvature tensor for Christoffel symbols identified with the structure constants. A subclass of isoassociative quantum deformations is described by the oriented associativity equation and, in particular, by the WDVV equation. It is demonstrated that a wider class of weakly (non)associative quantum deformations is connected with the integrable soliton equations too. In particular, such deformations for the three-dimensional and infinite-dimensional algebras are described by the Boussinesq equation and KP hierarchy, respectively.
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