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Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

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Abstract

In order to distinguish the connected graded Frobenius algebras determined by different twisted superpotentials, we introduce the nondegeneracy of twisted superpotentials. We give the sufficient and necessary condition for connected graded Frobenius algebras determined by two nondegenerate twisted superpotentials to be isomorphic. As an application, we classify the connected ℤ-graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.

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Acknowledgments

The authors thank the referee for his/her careful reading of the paper and useful suggestions.

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Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Siwangting Road 180, Yangzhou, Jiangsu, 225002, P. R. China

    Xuejun Xia & Libin Li

Authors
  1. Xuejun Xia
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  2. Libin Li
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Correspondence to Xuejun Xia.

Additional information

The research was supported by the National Natural Science Foundation of China (No. 11871063) and the Scientific Research and Innovation Project of Graduate Students in Jiangsu Province (No. KYCX21-3186).

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Xia, X., Li, L. Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials. Czech Math J 72, 1029–1044 (2022). https://doi.org/10.21136/CMJ.2022.0315-21

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  • DOI: https://doi.org/10.21136/CMJ.2022.0315-21

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