Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 72, No. 4, pp. 1029-1044, 2022

Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

Xuejun Xia, Libin Li

Received September 2, 2021. Published online May 12, 2022.

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 $\mathbb Z$-graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.

Keywords: graded Frobenius algebra; coalgebra; twisted superpotential

Classification MSC: 16W50, 16W55

DOI: 10.21136/CMJ.2022.0315-21

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Xuejun Xia (corresponding author), Libin Li, School of Mathematical Science, Yangzhou University, Siwangting Road 180, Yangzhou, Jiangsu 225002, P. R. China, e-mail: xiaxuejunmath@163.com, lbli@yzu.edu.cn

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