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Results tagged with weyl-algebra
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user 750
7
votes
1
answer
566
views
Depth Zero Ideals in the Homogenized Weyl Algebra
Let $\mathcal{D}$ be the $n$th Weyl algebra $ \mathcal{D} :=k[x_1,...,x_n,\partial_1,...,\partial_n] $, where $\partial_ix_i-x_i\partial_i=1$.
Let $\widetilde{\mathcal{D}}$ be its Rees algebra, whi …
- 13k
12
votes
1
answer
640
views
Does the image of a differential operator always contain an ideal?
Let $\delta$ denote a non-zero complex algebraic differential operator in a single variable x. That is, it can be written as a sum
$$ \delta = \sum_i f_i\partial_x^i$$
where there $f_i$ are complex p …
- 13k
10
votes
Proof a Weyl Algebra isn't isomorphic to a matrix ring over a division ring
A different proof would be to show that a Weyl algebra is not semisimple, that is, that it is not a direct sum of simple submodules as a left module over itself. However, note that there is an infini …
- 13k