Artin-Schelter regular algebras of dimension five with two generators.

DOI10.1016/J.JPAA.2013.10.011zbMATH Open1288.16039arXiv1303.1335OpenAlexW2058729300MaRDI QIDQ392520

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Publication date: 14 January 2014

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Abstract: We study and classify Artin-Schelter regular algebras of dimension five with two generators under an additional $mathbb{Z}^2$-grading by Hilbert driven Gr"{o}bner basis computations. All the algebras we obtained are strongly noetherian, Auslander regular, and Cohen-Macaulay. One of the results provides an answer to Fl{o}ystad-Vatne's question in the context of $mathbb{Z}^2$-grading. Our results also achieve a connection between Lyndon words and Artin-Schelter regular algebras.

Full work available at URL: https://arxiv.org/abs/1303.1335

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