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Skew Calabi-Yau property of normal extensions

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Abstract

We prove that the skew Calabi-Yau property is preserved under normal extension for locally finite positively graded algebras. We also obtain a homological identity which describes the relationship between the Nakayama automorphisms of skew Calabi-Yau locally finite positively graded algebras and their normal extensions. As a preliminary, we show that the Nakayama automorphisms of skew Calabi-Yau algebras always send a regular normal element to a multiple of itself by a unit.

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Acknowledgements

G.-S. Zhou is supported by the NSFC (Grant No. 11601480); Y. Shen is supported by the NSFC (Grant No. 11701515); D.-M. Lu is supported by the NSFC (Grant No. 11671351). The authors thank the referee for his/her careful reading and valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Ningbo University, Ningbo, 315211, China

    G.-S. Zhou

  2. Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Y. Shen

  3. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China

    D.-M. Lu

Authors
  1. G.-S. Zhou
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  2. Y. Shen
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  3. D.-M. Lu
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Correspondence to Y. Shen.

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Zhou, GS., Shen, Y. & Lu, DM. Skew Calabi-Yau property of normal extensions. manuscripta math. 161, 125–140 (2020). https://doi.org/10.1007/s00229-018-1064-6

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  • DOI: https://doi.org/10.1007/s00229-018-1064-6

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