Quantum deformations of associative algebras and integrable systems
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.
Keywords
Cite
@article{arxiv.0802.3022,
title = {Quantum deformations of associative algebras and integrable systems},
author = {B. G. Konopelchenko},
journal= {arXiv preprint arXiv:0802.3022},
year = {2009}
}
Comments
Numeration of the formulas is corrected