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Results tagged with derivations
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user 132126
A derivation on a ring 𝑅 is a map 𝐷:𝑅→𝑅 satisfying 𝐷(𝑎+𝑏)=𝐷(𝑎)+𝐷(𝑏) and 𝐷(𝑎𝑏)=𝑎𝐷(𝑏)+𝐷(𝑎)𝑏.
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Structure of the module of derivations on the space of Holomorphic functions
If you have a smooth manifold $M$, then you have a linear map $\mathfrak{X}(M) \to \text{Der}(C^{\infty}(M))$ from the space of smooth global vector fields to the space of derivations of the algebra of … Here is a proof of a similar result for real-analytic manifolds (real-analytic vector fields are exactly derivations of the algebra of real-analytic functions) by David Speyer. …
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