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Elliptic, parabolic and hyperbolic operators. Laplace, Laplace-Beltrami, Schrödinger, Dirac. Exterior derivative and Lie derivative operators.
18
votes
Accepted
Are there any natural differential operators besides $d$?
I think your question, the way it is stated, makes one want to classify unary and binary (depending how far you generalise the question as written) invariant differential operators on tensor fields. T …
2
votes
Accepted
Hochschild (co)homology of differential operators
It is not literally what you want, but very close: check Proposition 2.3 and related results in "A Riemann-Roch-Hirzebruch formula for traces of differential operators" by Markus Engeli and Giovanni F …
1
vote
Modules over rings of differential operators
If $A$ is an algebra, $M$ is a left $A$-module, and $B$ is an $A$-bimodule (e.g. $A$ itself, like in your example), then $Hom_A(M,B)$ is a right $A$-module, with the action given, as you suggest, by $ …