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10h
reviewed Leave Open Why is the kernel of an algebraic Hecke character open in the ideles?
10h
reviewed Approve Number of critical points of a smooth function
14h
reviewed Close Isomorphism between $\mathbb R^3$ and the the Heisenberg group
14h
comment Isomorphism between $\mathbb R^3$ and the the Heisenberg group
OK, so this is the polarized form. Is your question "how do I show the polarized form is isomorphic to the one using $\Im(\overline{z}w)$?
14h
comment Existence of a solution of a system of polynomial equations
This seems very open-ended. "Please give me conditions such that my result works" is, in my view, not a very good way to pursue research. What is the simplest special case that you would be interested in?
14h
comment Isomorphism between $\mathbb R^3$ and the the Heisenberg group
Hang on: it seems you are aware of the polarized versus unpolarized distinction math.stackexchange.com/questions/1684180/… So could you clarify what exactly are the two groups which you wish to show are isomorphic?
14h
comment Isomorphism between $\mathbb R^3$ and the the Heisenberg group
Z. Alfata, could you please clarify whether your definition of the Heisenberg group uses the formula quoted in your question, or the formula in your comment?
14h
comment Isomorphism between $\mathbb R^3$ and the the Heisenberg group
@Raziel I think the confusion here is that the OP is thinking of the Heisenberg group in polarized form (i.e. coming from the 3 by 3 matrix picture) while the version displayed in the question is the unpolarized form
15h
comment Isomorphism between $\mathbb R^3$ and the the Heisenberg group
I think you are misreading or misunderstanding something here. The point is that as a manifold the Heisenberg group is diffeomorphic to $R^3$. What you are presumably reading, in a book or a paper, is the statement that we can use the law you have written as a way to define a new group operation on $R^3$; equipped with this new group operation, $R^3$ becomes a Lie group $G$; and then more or less by construction, $G$ is isomorphic in the category of Lie groups and smooth group homomorphisms to the Heisenberg group.
15h
answered “Identity tensor transpose” as a map $M_n \hat{\otimes} M_n \to M_n \overline{\otimes} M_n$
21h
comment Is it possible to have a research career while checking the proof of every theorem that you cite?
I like this answer very much. Personally, as a reader and referee, I would prefer people to state clearly in separate theorems the parts which they are using from the literature, and which may be hard or obscure, rather than merely saying in the middle of a proof "By [13, Theorem 2.2] ..."
1d
comment Great Mathematicians Without a PhD
I think the question as currently phrased is too vague (you don't actually specifiy a time period) and subjective (what counts as "great"?). For instance, you mention Galois, but really the academic system was so different back then that it makes little sense to talk of PhDs then as if they are like PhDs in the post 1900-era. Nevertheless, since you ask, my canonical answer to this question is Uffe Haagerup (but only because he got a job offer without having to complete the PhD, if I understand correctly).
1d
revised Rational power Napier number
the previous edit seemed to change the tone/intent of the question; I have partially reverted
1d
comment Upper bound on the norm of the inverse of matrices with zero limit
I'm voting to close this question because it is already open on MSE and should get adequate answers there
1d
revised “Identity tensor transpose” as a map $M_n \hat{\otimes} M_n \to M_n \overline{\otimes} M_n$
updated the update
1d
reviewed Leave Closed Rational power Napier number
2d
reviewed Leave Closed Can the work of Hardy & Ramanujan about partitions shed light on Hardy-Littlewood's k-tuple conjecture?
2d
revised “Identity tensor transpose” as a map $M_n \hat{\otimes} M_n \to M_n \overline{\otimes} M_n$
updated
May
2
comment What is the group of automorphisms of $l^{\infty}$?
In the Cstar context, the characters of $\ell^\infty({\bf Z})$ are NOT all given by evaluation at integers -- rather, they correspond to points of the Stone-Cech compactification. I suspect that in your second paragraph you want to restrict attention to weak-star continuous characters, which are all of the form you state.
May
2
comment What is the group of automorphisms of $l^{\infty}$?
So do you require that the automorphisms are weak-star continuous? (This might come for free, but I haven't thought deeply about it)