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Artin-Schelter regular algebras of dimension five with two generators (1303.1335v1)
Published 6 Mar 2013 in math.RA
Abstract: We study and classify Artin-Schelter regular algebras of dimension five with two generators under an additional $\mathbb Z2$-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 $\mathbb Z2$-grading. Our results also achieve a connection between Lyndon words and Artin-Schelter regular algebras.
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