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location Buenos Aires
age 41
visits member for 5 years, 10 months
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Aug
29
comment cup product and Steenrod operations in Serre spectral sequence
What one does have is an algebra isomorphism of the gr of the limit with the E^2 page. In this example one sees exactly what gets lost when passing to the associated graded algebra.
Aug
28
comment $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
For $N$-Koszul modules you do need also the higher products. The cup product on $Ext_A(k,k)$ with $A$ $3$-Koszul is in fact zero. (I wrote Koszul but I was think of $N$-Koszul :-/ )
Aug
28
comment $Ext$-algebra generated by $Hom$ and $Ext^1$ as $A_\infty$-algebra?
This works for Koszul modules, iirc.
Aug
25
comment Are all separable algebras Frobenius algebras?
(I also implictly assumed you were in a context in which there is a ground ring around; it would certainly help if you emphasized in your question that this is not the case!)
Aug
25
comment Are all separable algebras Frobenius algebras?
One way to construct this is to look at the subsemigroup $\{0,1\}$ of the multiplicative semigroup of $\mathbb R$ with its induced order, turning it into a category as a poset and as a monoidal category using the semigroup structure.
Aug
23
awarded  Nice Answer
Aug
20
awarded  Nice Question
Jul
26
awarded  Good Answer
Jul
18
comment Commutative algebra books representing the edge of research
You should subscribe to arXiv announcements on that subject and, if you have access, browse MathSciNet.
Jul
16
comment Limits of complex projective varieties in the Hausdorff topology on closed subsets of CP^n
Ah. I am sorry. I thought you might be trying to be helpful. My mistake.
Jul
16
comment Limits of complex projective varieties in the Hausdorff topology on closed subsets of CP^n
But homogeneous polynomials do not "take values" on points of projective space.
Jul
10
comment Lie algebra cohomology with values in the ring of smooth functions of a $G$-manifold
The original version looked intriguing :-)
Jul
10
comment Lie algebra cohomology with values in the ring of smooth functions of a $G$-manifold
Your cocycles are just smooth maps? They are usually linear.
Jul
6
awarded  Guru
Jun
23
comment Do representations of the universal enveloping algebra $\mathrm{U}\mathfrak{su}_2$ retain the Hopf algebra structure?
In what way is your $U_J\mathfrak{su}_2$ an algebra?
Jun
23
comment Do representations of the universal enveloping algebra $\mathrm{U}\mathfrak{su}_2$ retain the Hopf algebra structure?
There are no Hopf algebras which are simple as algebras (except the ground field, of course), precisely because of the existence of the counit. On the other hand, there is no finite dimensional Hopf algebra over a field of characteristic zero with a non-zero primitive element.
May
28
awarded  Necromancer
May
27
comment Example of a $G$-sphere that is not a $G$-representation sphere
@QiaochuYuan, can a finite group not fix a smooth structure?
May
27
comment The construction of the 257gon
@FranzLemmermeyer, thanks! Do you know what the tables appearing in pictures 8 to 4 (counting from the last) are?
May
26
comment What is the exterior derivative intuitively?
@FallenApart, ah. No , I do not mean that $\Omega^1(M)$ is the module of Kähler differentials of $C^\infty(M)$ (mostly, because it isn't! :) ) The operator $d:C^\infty(M)\to\Omega^1(M)$ can be characterized in terms of its functorial properties. This is surely done in detail in the book Natural Operations in Differential Geometry by Kolar, Michor and Slovak.