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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.
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
Linking options:
https://www.mathnet.ru/eng/tmf210https://doi.org/10.4213/tmf210 https://www.mathnet.ru/eng/tmf/v136/i1/p20
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