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Apr 7 |
awarded | Guru |
Apr 7 |
revised |
What is special about polylogarithms that leads to so many interesting identities and applications?
small improvements/corrections |
Jan 25 |
awarded | Revival |
Nov 20 |
awarded | Yearling |
Nov 19 |
awarded | Good Question |
Nov 15 |
awarded | Notable Question |
Oct 5 |
asked | Pull back of D-modules and Koszul resolution |
Sep 29 |
awarded | Necromancer |
Sep 29 |
comment |
Hopf algebra structure on the ring of quasisymmetric functions
Indeed he is. Btw if you are looking for references on the subject, you should know that the product is often called the "stuffle product" (as it is somewhow opposite to the usual "shuffle product" of the Tensor Hopf algebra). |
Sep 10 |
revised |
Can I define the polynomial ring A[x] with an isomorphism f: A ---> A[x]?
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Aug 31 |
revised |
Hopf algebra structure on the ring of quasisymmetric functions
added 213 characters in body |
Aug 31 |
comment |
Hopf algebra structure on the ring of quasisymmetric functions
This is basic duality. Basically if you have a $k$-Hopf algebra $H$ with $k$-basis $h_s$ then $Hom_{k-mod}(H,A) = H^\vee \otimes_k A$. And, by duality, an element $\sum a_s h_s^\vee$ in this last $k$-module corresponds to a $k$-algebra morphism iff it is diagonal. Rather than paraphrasing what I remember about this stuff I added a link to a short simple article on the subject. |
Aug 31 |
comment |
Hopf algebra structure on the ring of quasisymmetric functions
I edited to answer your questions. |
Aug 31 |
revised |
Hopf algebra structure on the ring of quasisymmetric functions
added 201 characters in body |
Aug 31 |
answered | Hopf algebra structure on the ring of quasisymmetric functions |
Aug 29 |
comment |
Iterated Milnor fibrations and Thom's a_f condition
Thanks for the link, I had already glanced at it but I don't think it is relevant since they are only considering a dimension 1 base, i.e. a single function $f:X\to \mathbb C$. |
Aug 28 |
comment |
Poisson structure on the cotangent bundle
The problem is that you are forgetting the last axiom in B-B's definition of a TDO, namely how $gr^1 A$ is identified with $T_X$ through $\sigma(d)(f) = fd - df$. The Poisson bracket on the cotengant bundle is the equivalent of a first ordre non commutative deformation. A simple isomorphism of algebras $gr A \simeq Sym T_X$ forgets about this information. The Poisson bracket is just a Lie bracket that is also a derivation. To get the desired result you just have to check that $\sigma$ given in degree 1 extends uniquely to the whole symetric algebra. |
Aug 27 |
revised |
Microlocal geometry - A theorem of Verdier
edited tags |
Aug 27 |
comment |
Poisson structure on the cotangent bundle
Which definition of a sheaf of twisted differential operators are you working with? If you take the one from Beilinson and Bernstein, the isomorphism of Poisson structures is straightforward. |
Aug 27 |
comment |
Microlocal geometry - A theorem of Verdier
I posted the question quite a while ago, tried the bounty but still got no answer or comment. Is it because the problem is actually difficult or because the question is poorly formulated. I guess what seemed elementary to Verdier really isn't for most of us. Anyways, once again any comment, advice or reference would be truly appreciated. Thanks. |