Differential Operators on Smooth Manifolds
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The property of a differential operator on a smooth manifold M to be invariant with respect to an action of some group G (especially a Lie group) on M plays a great role in mathematical physics since it helps select physically significant operators. The algebra DiffG(M) of all G-invariant differential operators with complex or real coefficients on M gives the material for constructing G-invariant physical theories on M. Properties of such theory are in close connection with properties of the algebra DiffG(M).
KeywordsRiemannian Manifold Linear Subspace Smooth Manifold Isometry Group Symmetric Operator
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