Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 399–415 | Cite as

Double Frobenius algebras

Research Article
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Abstract

Some equivalent conditions for double Frobenius algebras to be strict ones are given. Then some examples of (strict or non-strict) double Frobenius algebras are presented. Finally, a sufficient and necessary condition for the trivial extension of a double Frobenius algebra to be a (strict) double Frobenius algebra is given.

Keywords

Double Frobenius algebra bi-Frobenius algebra trivial extension 

MSC

16W10 

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Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11471282), the China Postdoctoral Science Foundation (Grant No. 2017M610316), and the Natural Science Foundation of Jiangsu Province (Grant No. BK20170589).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Department of MathematicsTaizhou CollegeTaizhouChina
  3. 3.School of Mathematical ScienceYangzhou UniversityYangzhouChina

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