Reality in the Differential Calculus on q-euclidean Spaces

TL;DR

This paper explores the real structure of derivatives and differentials in euclidean q-spaces, constructing a real Laplacian and analyzing the reality properties of the exterior derivative.

Contribution

It introduces the nonlinear reality structure in derivatives and differentials for euclidean q-spaces and constructs a real Laplacian.

Findings

Real Laplacian constructed for q-euclidean spaces

Reality properties of the exterior derivative established

Nonlinear reality structure identified in derivatives

Abstract

The nonlinear reality structure of the derivatives and the differentials for the euclidean q-spaces are found. A real Laplacian is constructed and reality properties of the exterior derivative are given.