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On finite dimensional Jacobian algebras

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Abstract

We show that Jacobian algebras arising from every tagged triangulation of a sphere with n-punctures, with \(n\ge 5\), are finite dimensional algebras. We consider also a family of cyclically oriented quivers and we prove that, for any primitive potential, the associated Jacobian algebra is finite dimensional.

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Acknowledgments

The second author thanks Professor Michael Barot for discussing some central ideas for this article. She thanks Professor Christof Geiss for pointing out some important results on surfaces with non-empty boundary. She also thanks Daniel Labardini-Fragoso for clarifying ideas of his article [9]. We thank Daniel Labardini-Fragoso for his helpful comments and suggestions given in a preliminary version of this article. We also thank Ignacio Garcia for helping us with the figure of the sphere. The second author was partially supported by a CONICET doctoral fellowship.

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  1. Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Funes 3350, Universidad Nacional de Mar del Plata, 7600, Mar del Plata, Argentina

    Sonia Trepode & Yadira Valdivieso-Díaz

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  1. Sonia Trepode
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  2. Yadira Valdivieso-Díaz
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Correspondence to Yadira Valdivieso-Díaz.

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Trepode, S., Valdivieso-Díaz, Y. On finite dimensional Jacobian algebras. Bol. Soc. Mat. Mex. 23, 653–666 (2017). https://doi.org/10.1007/s40590-015-0082-6

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  • DOI: https://doi.org/10.1007/s40590-015-0082-6

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