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Symmetries in connected graded algebras and their PBW-deformations

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Abstract

We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo’s quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a \({{\cal K}_2}\) algebra \({\cal A}\) which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra \({\cal F}{{\cal K}_3}\), and explicitly construct all the (self-)symmetric and sign-(self-)symmetric PBW-deformations of \({\cal A}\).

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Acknowledgements

We would like to express our sincere gratitude to the referee for several helpful suggestions.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, 57 Jingxuan West Road, Qufu, Shandong, 273165, P. R. China

    Yongjun Xu & Xin Zhang

Authors
  1. Yongjun Xu
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  2. Xin Zhang
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Correspondence to Yongjun Xu.

Additional information

The research has been supported by the National Natural Science Foundation of China (Nos. 11501317, 12271292), the China Postdoctoral Science Foundation (No. 2016M600530), and the Project of Qufu Normal University (No. BSQD20130142).

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Xu, Y., Zhang, X. Symmetries in connected graded algebras and their PBW-deformations. Czech Math J 73, 1255–1272 (2023). https://doi.org/10.21136/CMJ.2023.0511-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0511-22

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