Abstract
We study and classify Artin–Schelter regular algebras of dimension five with two generators under an additional Z2-grading by Hilbert driven Gröbner basis computations. All the algebras we obtained are strongly noetherian, Auslander regular, and Cohen–Macaulay. One of the results provides an answer to Fløystad–Vatneʼs 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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