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Results tagged with d-modules
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user 345
Modules over rings of differential operators.
5
votes
Accepted
Testing ideal membership in the Weyl algebra: a simple example
Following my nose gave the following argument. Writing $I$ be the left ideal generated by $x\partial^2$ and $x^3$ and using $\cdot$ to stress multiplication we get
$$ x^2 \cdot x\partial^2 - \partia …
- 3,545
10
votes
Accepted
What kind of algebraic object is $\mathcal{D}_X$? (algebra of diifferential operators). What...
Proposition 1.2.9 of http://math.columbia.edu/~scautis/dmodules/hottaetal.pdf explains that if $M$ and $N$ are both left $D$-modules and $M'$ and $N'$ are both right $D$-modules then
(a) $M\otimes_{ …
- 3,545
10
votes
Why should the tensor product of $\mathcal{D}_X$-modules over $\mathcal{O}_X$ be a $\mathcal...
One way to think about this is that $D$ is the universal enveloping algebra $U(R,L)$ of the $(k,R)$ Lie-Rinehart algebra $\mathrm{Der}_k(R,R)$. Whenever one has such an enveloping algebra one may perf …
- 3,545