Reputation
Next tag badge:
538/400 score
79/80 answers
Badges
19 239 519
Newest
 polynomials
Impact
~2.8m people reached

27m
awarded  polynomials
2d
comment Holomorphic contractibility of GL(H)?
What do "holomorphically contractible" and "holomorphic $K(\mathbb{Z}, 2)$" mean?
2d
comment Time-Energy Uncertainty Relation in relativistic Quantum Mechanics
Probably going to get better answers on physics.stackexchange.com.
May
1
awarded  Enlightened
Apr
30
awarded  Nice Answer
Apr
30
comment Maps from $S^3$ to $S^3$
For what it's worth, I didn't downvote, but you're not doing yourself any favors by insulting people and questioning their expertise. Denis is correct that there is a notion of polynomial map in this setting, namely a map all of whose coordinates are given by polynomials (thinking of $S^3$ as embedded in $\mathbb{R}^4$ in the usual way); for example, the maps $z \mapsto z^n$ coming from the group structure on $SU(2)$ are polynomial maps in this sense. For a discussion of degree see, for example, en.wikipedia.org/wiki/Degree_of_a_continuous_mapping.
Apr
30
comment Maps from $S^3$ to $S^3$
The space of maps has connected components labeled by degree, which is an integer. Is this the sort of thing you want to know? Right now your question is very vague.
Apr
30
comment From Weyl groups to Weyl groupoids?
It's easier to have this discussion on the Lie group rather than Lie algebra level. There for $G$ a compact connected Lie group you can consider the groupoid whose objects are maximal tori and whose morphisms are conjugations. Every object in this groupoid is isomorphic, and all of their automorphism groups are the Weyl group.
Apr
30
comment “Small” simplicial complex with torsion trees
So just to clarify, these spanning trees are not in fact trees?
Apr
29
answered Representation viewpoint on Chern Weil (cohomology computations done with rep theory?)
Apr
29
comment what is the universal cover of GL(2,R)?
The OP also says "and therefore $G'$ was $\mathbb{C}^2$" so I think it is clear he meant $\mathbb{C}^{\ast} = \mathbb{C} \setminus \{ 0 \}$. (I prefer the notation $\mathbb{C}^{\times}$.)
Apr
28
comment what is the universal cover of GL(2,R)?
$GL_2^{+}(\mathbb{R})$, as a manifold, is $\mathbb{R}^3 \times SO(2)$. (More generally, any connected Lie group, as a manifold, is its maximal compact times some $\mathbb{R}^n$.) So its universal cover, as a manifold, is $\mathbb{R}^4$.
Apr
28
comment Does it make sense to compare sets (polytopes) with different dimensions?
@Dima: I don't know what that means. The OP claims to have proven a statement and then wants to know whether the statement makes sense. If the OP doesn't know whether it makes sense then how did they prove it?
Apr
26
comment “Spatial (geometrical)” realization of Elementary topos?
@Simon: yes, I required the tensor product to distribute over colimits above. Elementary topoi can be ind-completed and I think the result is now monoidal cocomplete although I haven't checked this.
Apr
26
comment “Spatial (geometrical)” realization of Elementary topos?
@Andrej: well, that's stronger than an analogy, right? One is even a special case of the other. I really just mean an analogy here. It's very naive: colimits are like addition. A more precise analogy would have been to commutative monoids since coproducts don't have inverses. For example, like in commutative monoids, there is a zero object, and biproducts. In this analogy presheaf categories are analogous to free abelian groups.
Apr
26
revised “Spatial (geometrical)” realization of Elementary topos?
added 89 characters in body
Apr
26
answered “Spatial (geometrical)” realization of Elementary topos?
Apr
26
answered Probability theory without deductive closure
Apr
26
comment When are Morita classes represented by certain structured algebra objects?
Also, depending on what you mean by "semisimple module category," I don't think your claim that these are all categories of modules over algebras is true either, since (with the definitions I have in mind) there may be infinitely many simple objects.
Apr
26
comment When are Morita classes represented by certain structured algebra objects?
I don't understand your example in the second paragraph. It's certainly not the case that every algebra is Morita equivalent to a Clifford algebra. I think you're missing some hypotheses? Similarly, it's certainly not the case that every algebra is semisimple. Maybe you could be more explicit about exactly what your definitions are?