An example of a quadratic AS-regular algebra without any point modules

Abstract

Although it has been known for decades that a quadratic AS-regular algebra of global dimension  n n need not have any point modules if n ≥ 5 n \geq 5 , an explicit example appears to be absent, prior to the present article, from the published literature. This situation was brought to the attention of the author by the anonymous referee of D. Rogalski’s survey article Artin-Schelter Regular Algebras, who encouraged the author of the present article to remedy the situation. Consequently, an explicit example is presented herein of a quadratic AS-regular algebra of global dimension five that is a graded Clifford algebra having no point modules.