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arXiv · 0802.3022

Quantum deformations of associative algebras and integrable systems

B. G. Konopelchenko
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Abstract

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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B. G. Konopelchenko. 2008-04-28. Quantum deformations of associative algebras and integrable systems. https://doi.org/10.1088/1751-8113%2F42%2F9%2F095201

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