Geometry of Regular Algebras of Global Dimension 4 related to Graded Skew Clifford Algebras of Global Dimension 3

TL;DR

This paper investigates the geometric properties of certain regular algebras of global dimension 4, specifically those related to graded skew Clifford algebras of dimension 3, by computing their point schemes.

Contribution

It introduces a method to compute point schemes of regular algebras related to graded skew Clifford algebras using computational tools.

Findings

Computed point schemes for specific regular algebras

Established connections between algebras of dimensions 3 and 4

Demonstrated the use of Mathematica in algebraic geometry

Abstract

We compute point schemes of some regular algebras using (Wolfram) Mathematica. These algebras are Ore extensions of regular graded skew Clifford algebras of global dimension 3.