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location Buenos Aires
age 40
visits member for 4 years, 10 months
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19h
comment q-th powers and roots of polynomials
@grok, it is best to put information asuch as that you gice in the comment in the question body itself :-)
1d
awarded  Nice Answer
Aug
16
accepted The octonions on a bad day
Aug
12
comment Identities that connect antipode with multiplication and comultiplication
Those identities are usually described by saying that the antipode map is an antihomomorphism of coalgebras and of algebras, and should be proved in most textbooks on the subject.
Aug
3
comment when is the restriction $H^2(G,\mathbb{C}^*)\to H^2(K,\mathbb{C}^*)$ surjective?
When G is abelian or, more generally, when K is normal, somrthing can be said by looking at the Leray Hochschild Serre spextral sequence.
Jul
23
comment Noncommutative HKR theorem
They are not the same.
Jul
23
awarded  Nice Answer
Jul
22
comment Noncommutative HKR theorem
Daniel is right in that a sensible definition of forms in the nc world is through Hochschild homology (or the actual Hochschild complex); this is the point of the noncommutative calculi of Tsygan, Tamarkin and others. It is also true that for other (closely related!) purpuses one uses the definition mentioned by Sasha in his comment above. You can read about it in Max Karoubi's Astérique on cyclic homology, among other places.
Jul
20
comment A few questions about Kontsevich formality
Great answer :-)
Jul
17
comment How weird can Modular Tensor Categories be over non-algebraically closed fields?
A recent result of Ehud Meir is that the Schur group constructed out of semisimple Hopf algebras is in fact the whole Brauer group, son one can get all CSAs if we allow for general Hopf algebras instead of just groups.
Jul
13
comment What kind of algebra is the class of ordered pairs equipped with the binary operation which forms them?
Out of curiosity: is there an ordered-pair definition which does not raise the rank?
Jul
12
comment Why are we interested in the Fundamental Groupoid of a Space?
Have you searched in this site (and in math.stackexchange.com) for relevant questions and answers? I am sure this has been discussed before —in particular, by Ronnie Brown.
Jul
11
comment (Krull) dimension of any associated graded ring of a ring R equals the dimension of R
@CSA, you can find en C&E or in Weibel or in many other places a construction of the Chevalley-Eilenberg resolution of the trivial left module of an enveloping algebra. There is an analogue of that for bimodules.
Jul
11
comment (Krull) dimension of any associated graded ring of a ring R equals the dimension of R
@CSA, that algebra is the enveloping algebra of the unique non-abelian Lie algebra of dimension 2. It's global dimension is equal to is bimodule projective dimension is equal to 2.
Jul
11
comment (Krull) dimension of any associated graded ring of a ring R equals the dimension of R
@CSA, it is not true, so no :-). For example, suppose $2\neq0$ in the field $k$; then the algebra $k[x]/(x^2-1)$ has zero dimension as a bimodule over itself, yet there is an increasing filtration on it such that the associated graded algebra is $k[x]/(x^2)$, which has infinite H dimension. In any case, there are several different things you can mean by «analogous»...
Jul
10
comment When is separation of variables an acceptable assumption to solve a PDE?
But one rarely solves a PDE by separating variables in the boundary conditions: one usually finds eigensolutions and does a series development.
Jul
8
comment A parametrization of subsets
Thanks! ${}{}{}$
Jul
8
comment Why localize spaces with respect to homology?
One old (I don't like the adverb cowardly...) construction of localizing modulo a functor is localization modulo torsion of abelian groups, à la Serre.
Jul
8
comment Why localize spaces with respect to homology?
The localization at E is a description of what E sees: one has as much hope in it being useful as one trusts E to provide useful information, no?
Jul
8
comment A parametrization of subsets
@JosephO'Rourke, yup! Thanks.