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REGULARITY CRITERION AND CLASSIFICATION FOR ALGEBRAS OF JORDAN TYPE
Published online by Cambridge University Press: 21 July 2015
Abstract
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.
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- Copyright © Glasgow Mathematical Journal Trust 2015
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