Point modules over regular graded skew Clifford algebras

Abstract

Results of Vancliff, Van Rompay and Willaert in 1998 [8] prove that point modules over a regular graded Clifford algebra (GCA) are determined by (commutative) quadrics of rank at most two that belong to the quadric system associated to the GCA. In 2010, in [4], Cassidy and Vancliff generalized the notion of a GCA to that of a graded skew Clifford algebra (GSCA). The results in this article show that the results of [8] may be extended, with suitable modification, to GSCAs. In particular, using the notion of μ-rank introduced recently by the authors in [9], the point modules over a regular GSCA are determined by (noncommutative) quadrics of μ-rank at most two that belong to the noncommutative quadric system associated to the GSCA.