The Linear algebra in the quaternionic pluripotential theory

TL;DR

This paper simplifies and clarifies the linear algebra foundational to quaternionic pluripotential theory, enabling easier proofs and deeper understanding of key operators like the Moore determinant and quaternionic Monge-Ampère operator.

Contribution

It characterizes and normalizes real 2-forms under quaternionic structure and links the Moore determinant to exterior products of associated forms.

Findings

Characterization and normalization of real 2-forms in quaternionic setting

Connection between Moore determinant and exterior product coefficients

Simplification of proofs in quaternionic pluripotential theory

Abstract

We clarify the linear algebra used in the quaternionic pluripotential theory so that proofs of several results there can be greatly simplified. In particular, we characterize and normalize real $2$-forms with respect to the quaternionic structure, and show that the Moore determinant of a quaternionic hyperhermitian matrix is the coefficient of the exterior product of the associated real $2$-form. As a corollary, the quaternionic Monge-Amp\`{e}re operator is the coefficient of the exterior product of the Baston operator.