2008/02/29 by B. G. Konopelchenko · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Associative property #Curvature #Geometry #Integrable system #Mathematical physics #Mathematics #Noncommutative geometry #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum #Quantum group #Quantum mechanics #Riemann hypothesis #math-ph #math.MP #math.RA #nlin.SI
paper · pdf · doi:10.1088/1751-8113/42/9/095201
Numeration of the formulas is corrected
arxiv created 2008/04/28 · openalex publication_date 2009/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 have a geometrical meaning of a 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 Witten–Dijkgraaf–Verlinde–Verlinde 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.