Lie and Nijenhuis brackets on affine spaces
Abstract
Lie algebras are extended to the affine case using the heap operation, giving them a definition that is not dependent on the unique element 0, such that they still adhere to antisymmetry and Jacobi properties. It is then looked at how Nijenhuis brackets function on these Lie affgebras and demonstrated how they fulfil the compatibility condition in the affine case.
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