Geodesic
Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature
Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 1, pp. 20-29

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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.
Mots-clés : quasi-Frobenius algebra
Keywords: 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. 
@article{TMF_2003_136_1_a1,
     author = {O. I. Mokhov},
     title = {Quasi-Frobenius {Algebras} and {Their} {Integrable} $N${-Parameter} {Deformations} {Generated} by {Compatible} $(N\times N)$ {Metrics} of {Constant} {Riemannian} {Curvature}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {136},
     number = {1},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2003_136_1_a1/}
}
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O. I. Mokhov. Quasi-Frobenius Algebras and Their Integrable $N$-Parameter Deformations Generated by Compatible $(N\times N)$ Metrics of Constant Riemannian Curvature. Teoretičeskaâ i matematičeskaâ fizika, Tome 136 (2003) no. 1, pp. 20-29. http://geodesic.mathdoc.fr/item/TMF_2003_136_1_a1/