A Note on Generic Clifford Algebras of Binary Cubic Forms

Abstract

We study the representation theoretic results of the binary cubic generic Clifford algebra C, which is an Artin-Schelter regular algebra of global dimension five. In particular, we show that C is a PI algebra of PI degree three and compute its point variety and discriminant ideals. As a consequence, we give a necessary and sufficient condition on a binary cubic form f for the associated Clifford algebra C f to be an Azumaya algebra.2010 Mathematics Subject Classification. 16G30, 16R99.

A moduli interpretation of untwisted binary cubic forms

“…Wang and Wu showed that it is an Artin-Schelter regular, strongly noetherian, Auslander regular, Cohen Macauly algebra of global dimension 5 [36]. Its representation theoretic properties were explored by Wang and Wang in [35]. We explore other algebraic properties of A in Section 1.…”