Inner derivations are specific types of derivations in a non-associative algebra that can be expressed in terms of the multiplication operation with a fixed element from the algebra. More formally, for an algebra A and an element x in A, the inner derivation associated with x is defined as the mapping D_x: A → A, given by D_x(a) = x * a - a * x, where * denotes the multiplication operation. This concept connects closely to the structure of Lie algebras, as inner derivations play a role in understanding their properties and relationships.
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