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Quantum deformations of associative algebras and integrable systems | | B.G.Konopelchenko
; | | Date: |
21 Feb 2008 | | 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. | | Source: | arXiv, 0802.3022 | | Services: | Forum | Review | PDF | Favorites | |
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