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TMF, 2003, Volume 136, Number 1, Pages 20–29 (Mi tmf210)  

This article is cited in 3 scientific papers (total in 3 papers)

Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature

O. I. Mokhov

Landau Institute for Theoretical Physics, Centre for Non-linear Studies

Abstract: We prove that the equations describing compatible $(N\times N)$ metrics of constant Riemannian curvature define a special class of integrable $N$-parameter deformations of quasi-Frobenius (in general, noncommutative) algebras. We discuss connections with open-closed two-dimensional topological field theories, associativity equations, and Frobenius and quasi-Frobenius manifolds. We conjecture that open-closed two-dimensional topological field theories correspond to a special class of integrable deformations of associative quasi-Frobenius algebras.

Keywords: quasi-Frobenius algebra, Frobenius algebra, integrable deformation of an algebra, topological field theory, compatible metrics, constant-curvature metrics, integrable system, quasi-Frobenius manifold, Frobenius manifold, flat pencil of metrics, associativity equations

DOI: https://doi.org/10.4213/tmf210

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English version:
Theoretical and Mathematical Physics, 2003, 136:1, 908–916

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Received: 24.09.2002

Citation: O. I. Mokhov, “Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature”, TMF, 136:1 (2003), 20–29; Theoret. and Math. Phys., 136:1 (2003), 908–916

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Chang JH, “On the waterbag model of dispersionless KP hierarchy”, Journal of Physics A-Mathematical and General, 39:36 (2006), 11217–11230  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Chang, JH, “On the waterbag model of the dispersionless KP hierarchy (II)”, Journal of Physics A-Mathematical and Theoretical, 40:43 (2007), 12973  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    3. O. I. Mokhov, “Pencils of compatible metrics and integrable systems”, Russian Math. Surveys, 72:5 (2017), 889–937  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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