Artin-Schelter regular algebras of dimension five with two generators
Abstract
We study and classify Artin-Schelter regular algebras of dimension five with two generators under an additional Z2-grading by Hilbert driven Gr\"obner basis computations. All the algebras we obtained are strongly noetherian, Auslander regular, and Cohen-Macaulay. One of the results provides an answer to Flystad-Vatne's question in the context of Z2-grading. Our results also achieve a connection between Lyndon words and Artin-Schelter regular algebras.
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