Geodesic
REGULARITY CRITERION AND CLASSIFICATION FOR ALGEBRAS OF JORDAN TYPE
Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 69-95

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DOI

We show that Artin–Schelter regularity of a $\mathbb{Z}$-graded algebra can be examined by its associated $\mathbb{Z}$r-graded algebra. We prove that there is exactly one class of four-dimensional Artin–Schelter regular algebras with two generators of degree one in the Jordan type. This class is strongly noetherian, Auslander regular, and Cohen–Macaulay. Their automorphisms and point modules are described. 
SHEN, Y.; ZHOU, G.-S.; LU, D.-M. REGULARITY CRITERION AND CLASSIFICATION FOR ALGEBRAS OF JORDAN TYPE. Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 69-95. doi: 10.1017/S0017089515000075
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     author = {SHEN, Y. and ZHOU, G.-S. and LU, D.-M.},
     title = {REGULARITY {CRITERION} {AND} {CLASSIFICATION} {FOR} {ALGEBRAS} {OF} {JORDAN} {TYPE}},
     journal = {Glasgow mathematical journal},
     pages = {69--95},
     year = {2016},
     volume = {58},
     number = {1},
     doi = {10.1017/S0017089515000075},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089515000075/}
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