Artin-Schelter regular algebras of dimension five with two generators

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.