Structure preserving transformations in hyperkahler Euclidean spaces

TL;DR

This paper fully characterizes the invariance Lie algebra of hyperkahler structure preserving transformations in Euclidean spaces across all dimensions, advancing understanding of quaternionic symmetries.

Contribution

It provides a complete description of the invariance Lie algebra for hyperkahler structures in Euclidean spaces, extending previous partial results.

Findings

Complete structure of the invariance Lie algebra in Euclidean hyperkahler spaces.

Applicable to all dimensions, broadening the scope of previous studies.

Enhances understanding of quaternionic symmetry groups.

Abstract

The definition and structure of hyperkahler structure preserving transformations (invariance group) for quaternionic structures have been recently studied and some preliminary results on the Euclidean case discussed. In this work we present the whole structure of the invariance Lie algebra in the Euclidean case for any dimension.