Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups

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Abstract
This is the first of two papers in which the authors give a complete classification of symmetry reduced solutions of Plebanski’s potential equation for self-dual Einstein spaces. In this first part the infinite pseudogroup of symmetries of Plebanski’s equation is described, and the conjugacy classes of all local subgroups of dimensions one, two, and three over both the real and complex numbers are classified. Then in the second paper, this classification is used to obtain all symmetry-reduced solutions.

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