Embedding a quantum rank three quadric in a quantum P³

Abstract

We continue the classification, begun in [11], [14] and [12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadric hypersurfcice in P³. In this paper, we consider those cases where the quadric has rank 3. We also give sufficient conditions for the point scheme of any quadratic regular algebra of global dimension 4 to be the graph of an automorphism.

Keywords:

• Regular algebra
• quadratic algebra
• point scheme

1991 Mathematics Subject Classification:

• 16W50
• 16P40
• 14A22

^*The second author was supported in part by NSF grant DMS-9622765.

^*The second author was supported in part by NSF grant DMS-9622765.

Notes

^*The second author was supported in part by NSF grant DMS-9622765.