14
votes
0answers
392 views
+200

Explicit path in the unitary group of a $C^*$-algebra

For $G$ a discrete group, there is a canonical inclusion $g\mapsto u_g$ of $G$ into the unitary group of the reduced $C^*$-algebra $C^*_r(G)$. Denote by $[u_g]$ the class of $u_g$ in the (topological) ...
11
votes
2answers
831 views
+300

Elliptic Curves with CM and Class Field Theory

Let $K$ be an imaginary quadratic field with Hilbert class field $H$, and let $E$ be an elliptic curve defined over $H$ with complex multiplication by the ring of integers $O_K$ of $K$. It is known ...
6
votes
1answer
155 views
+100

On the convexity of certain integrals involving Bessel functions

Let $n\geq 0$ be an integer and let $J_n=J_n(r)$ denote the usual Bessel function (of the first kind) of order $n$ i.e. one of the solutions to Bessel's differential equation ...
5
votes
0answers
120 views
+50

Projective modules over noncommutative tori?

It is a theorem of Rieffel that for any simple noncommutative tori ($\mathcal{A}$) of dimension $n$, every projective module over it is isomorphic to direct sum of $\mathcal{S}(M)$, Schwartz class ...
1
vote
0answers
151 views
+50

Pullback of a sheaf associated to a divisor

I am reading a paper Desingularisation des varietes de Schubert generalisees by Demazure. I am interested in Lemma 3 on page 58. In particular, I would like to know whether the lemma is true and how ...
9
votes
0answers
145 views
+100

$2$-group with two isomorphic normal subgroups of index $4$ with non-isomorphic quotients

Hypothesis: Let $P$ be a finite $2$-group with two isomorphic normal subgroups $M$ and $N$ such that $P/M\cong C_4$ (the cyclic group of order $4$) while $P/N\cong C_2^2$. By the lattice theorem, ...
15
votes
4answers
368 views
+100

Is the diameter of a centrally symmetric convex body realized by a pair of antipodal points?

Let $S \subset \mathbb{R}^n$ be the boundary of a centrally symmetric convex body and provide $S$ with the geodesic metric given by its embedding in Euclidean space (i.e., the distance between two ...
5
votes
0answers
392 views
+50

Continued fraction representation of Zeta

A question at math.SE is asking for references. The fraction is quite nice! Check it out and post some references if you know of any. I found this at arxiv, but it doesn't apply to Zeta.
1
vote
0answers
197 views
+100

Topological razors (ball-like spaces)

Introduction Many admire the Euclidean space, and I am not an exception. I will try to catch the topological roundness of the $n$-ball in its greatest generality. I call the resulting axiomatized ...