Abstract:

To every (commutative) quadratic form is associated a symmetric matrix, and one has the standard notions of rank and determinant function defined on the matrix, and, thus, on the quadratic form. In a recent paper by T. Cassidy & M. Vancliff, the authors extend the notion of quadratic form to the noncommutative setting and introduce a quantized analog of a graded Clifford algebra called a graded skew Clifford algebra (GSCA). In this talk, we use our notion of mu-rank defined on noncommutative quadratic forms (in Vancliff & Veerapen, 2012) to show that the point modules over a regular GSCA are determined by (noncommutative) quadrics of mu-rank at most two that belong to the noncommutative quadric system associated to the GSCA.