Non-commutative Grassmann variety as a moduli space

TL;DR

This paper introduces a non-commutative analogue of the Grassmann variety G(2,4), framing it as a moduli space of linear subspaces within a projective space, expanding the geometric understanding into non-commutative realms.

Contribution

It constructs a non-commutative version of G(2,4) as a moduli space, providing a new perspective on non-commutative algebraic geometry.

Findings

Defined a non-commutative Grassmann variety G(2,4)

Established its interpretation as a moduli space of linear subspaces

Extended classical geometric concepts into non-commutative settings

Abstract

We construct a non-commutative version of the Grassmann variety $G(2,4)$ as a non-commutative moduli space of linear subspaces in a projective space.