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arXiv · 1303.1335

Artin-Schelter regular algebras of dimension five with two generators

G. -S. Zhou·D. -M. Lu
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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.

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BibTeXRIS

G. -S. Zhou, D. -M. Lu. 2013-03-06. Artin-Schelter regular algebras of dimension five with two generators. https://arxiv.org/abs/1303.1335

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