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Apr
25
comment Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
@Kally what is your working definition of polynomial differential operators, if not the algebra generated by $x_i, \partial_j$ subject to the above relations? There are several equivalent definitions, so the answer depends on which you take as fundamental.
Apr
25
answered Reference request for “Hodge Theorem”
Apr
15
answered Symplectic positive definite matrix.
Apr
14
comment Embedding/Submersion Properties of Cotangent Maps (Pullbacks)
Yes, $d\phi$ (or $\phi_\ast$, or $T\phi$) is the differential of $\phi$. I think (4) should be true as well, since $\phi$ will be a diffeomorphism on the total spaces and it is linear on the fibers.
Apr
14
answered Embedding/Submersion Properties of Cotangent Maps (Pullbacks)
Apr
13
comment Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
Updated to include a sketch of the proof. You can find the details in the lecture notes by Cannas da Silva.
Apr
13
revised Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
added 1002 characters in body
Apr
13
answered formal glueing of schemes
Apr
12
comment Exactness Axiom of Homology Theory
$C_k(\cdot)$ are the chains, with boundary map $\partial: C_k(\cdot) \to C_{k-1}(\cdot)$, so that $H_k = \ker \partial_k / \mathrm{im} \partial_{k+1}$. They depend on what homology theory you are considering, but they are always there in the background somewhere. For the singular homology of a space $X$ they are formal linear combinations of maps $\Delta^k \to X$ where $\Delta^k$ is the standard $k$-simplex. For simplicial and cellular homology there are analogous definitions. Whenever you encounter any kind of homology you should think of it as the homology of some underlying chain complex.
Apr
9
answered subgroup problem in abstract algebra
Apr
8
comment Center of Clifford Algebra depending on the parity of $\dim V$?
The parity issue is discussed in detail in E. Meinrenken's Notes math.toronto.edu/mein/teaching/clif_main.pdf . See Proposition 2.6 in particular, which gives the result over $\mathbb{C}$. Another good reference is Chevalley's book.
Apr
8
revised Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
small commment added
Apr
8
answered Why is $W(V)\simeq D(k[X_1,\dots,X_n])$?
Apr
7
answered Exactness Axiom of Homology Theory
Mar
16
answered Structure Sheaf on Scheme
Feb
13
answered Fourier transform of gaussian times polynomial to a high power
Feb
9
comment Non-closed subgroups of Lie groups
Irrational flows on the torus are well-studied (and famous) examples in noncommutative geometry. So it might be worth looking at the noncommutative geometry literature to see if there is anything like what you're asking.
Feb
4
comment Expressing Differential Form in Different Coordinates
@Confused I edited it to include a few more details of the evaluation of the pushforward.
Feb
4
awarded  Editor
Feb
4
revised Expressing Differential Form in Different Coordinates
added some extra detail