Infinitesimal Bäcklund transformations and Kac–Moody algebras in general relativity

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Abstract
Infinitesimal Bäcklund transformations are found for the problem of classical general relativity in d dimensions, which by dimensional reduction may be interpreted as gravitation interacting with several Maxwell and scalar fields. The transformations are constructed in terms of the solution of a linear system whose integrability condition yields the original field equations. The Kac–Moody algebra, which generates those transformations, is analyzed.