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Derivation (abstract Algebra)




: ''D'' : ''A'' → ''A''

that satisfies Leibniz' Law :

D


If ''A'' is Unital , then ''D''(1) = 0 since

D


Examples of derivations are Partial Derivative s, Lie Derivative s, the Pincherle Derivative , and the Commutator with respect to an element of the algebra. All these examples are tightly related, with the concept of derivation as the major unifying theme.


GRADED DERIVATIONS




  :''D''(''ab'') (''Da'')''b'' + (&minus1)<sup>''a''</sup>''a''(''Db'')