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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 …
Vladimir Dotsenko's user avatar
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 …
Vladimir Dotsenko's user avatar
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 $ …
Vladimir Dotsenko's user avatar