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Abstract

Using analytic methods of finite-gap integration, we construct quasihomogeneous algebraic solutions of the WDVV associativity equations and the nonsemisimple Frobenius manifolds associated with them.

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References

  1. I. M. Krichever, Funct. Anal. Appl., 31, 25–39 (1997).

    Article  MATH  MathSciNet  Google Scholar 

  2. R. Dijkgraaf, E. Verlinde, and H. Verlinde, Nucl. Phys. B, 352, 59–86 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Barannikov and M. Kontsevich, Internat. Math. Res. Notices, No. 4, 201–215 (1998).

  4. V. Shramchenko, Comm. Math. Phys., 256, 635–680 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. B. Dubrovin, “Geometry of 2D topological field theories,” in: Integrable Systems and Quantum Groups (Lect. Notes Math., Vol. 1620, M. Francaviglia et al., ed.), Springer, Berlin (1995), p. 120–348.

    Chapter  Google Scholar 

  6. E. Witten, Nucl. Phys. B, 340, 281–332 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  7. B. Dubrovin, Nucl. Phys. B, 379, 627–689 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  8. V. E. Zakharov, Duke Math. J., 94, 103–139 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  9. A. E. Mironov and I. A. Taimanov, Tr. Mat. Inst. Steklova, 255, 180–196 (2006).

    Google Scholar 

  10. A. Marshakov, A. Mironov, and A. Morozov, Phys. Lett. B, 389, 43–52 (1996).

    Article  ADS  MathSciNet  Google Scholar 

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 2, pp. 195–206, May, 2007.

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Mironov, A.E., Taimanov, I.A. Some algebraic examples of Frobenius manifolds. Theor Math Phys 151, 604–613 (2007). https://doi.org/10.1007/s11232-007-0047-7

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  • DOI: https://doi.org/10.1007/s11232-007-0047-7

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