Gaeta, G.Rodríguez González, Miguel Ángel2023-06-182023-06-182016-020393-044010.1016/j.geomphys.2015.11.004https://hdl.handle.net/20.500.14352/24394© 2015 Elsevier B.V. MAR was supported by the Spanish Ministry of Science and Innovation under project FIS2011-22566. GG is supported by the Italian MIUR-PRIN program under project 2010-JJ4KPA. This article was started in the course of visits of GG at Universidad Complutense of Madrid and of MAR at Università degli Studi di Milano.The definition and structure of hyperkähler 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.engjournal articlehttp://dx.doi.org/10.1016/j.geomphys.2015.11.004http://www.sciencedirect.comhttp://www.arxiv.orgopen access53-71Hyperkahler manifoldsHyperhamiltonian dynamicsCanonical transformationsInvariance algebra.Física (Física)22 Física