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0
votes
0answers
3 views

Is it true that $$( V \otimes^{max}W)^+=V^+ \otimes^ {max} W^+$$

For any $C^*-$ algebra $V$ assume that $V^+$ denotes the unitization of $V$. Let $V$ and $W$ be two $C^*-$ algebras then is it true that $$( V \otimes^{max}W)^+\cong V^+ \otimes^ {max} W^+$$ I guess ...
0
votes
0answers
12 views

Dense Stein subset in complex manifold

Let $X$ be a smooth proper algebraic variety. Then $X$ has a dense affine open subset. In particular, any smooth proper algebraic variety has a dense Stein open subset as the complement of a divisor. ...
-3
votes
0answers
12 views

Find a strong connected components for the graph [on hold]

I need a help with a homework of discrete mathematics, I’ll be really grateful for anyone who will be able to help me https://3.top4top.net/p_1245ww3160.jpg Thanks for everybody
0
votes
0answers
45 views

First homology group of the general linear group

The abelianization of the general linear group $GL(n,\mathbb{R})$ defined by $GL(n)^{ab} := GL(n)/[GL(n), GL(n)]$ is isomorphic to $\mathbb{R}^{\times}$. This follows from the fact that $[GL(n),GL(n)] ...
0
votes
0answers
16 views

About the Zassenhaus's filtration of a group G

The $n$-th term of the filtration of Zassenhaus of a group $G$, denoted by $D_n(G)$, is the subgroup generated by all $p^k$-th power of an element $x\in \gamma_i(G)$ such that $ip^k$ is greater or ...
1
vote
1answer
44 views

Non-standard tensor products of inner product spaces

For two inner product spaces $(\mathcal{V}, (\cdot,\cdot)_V)$ and $(\mathcal{W}, (\cdot,\cdot)_W)$, we can put an inner product on their tensor product in the obvious way: $$ (1) ~~~~ \langle v \...
2
votes
2answers
133 views

Tricks for getting a creative idea [on hold]

Caveat: I fear that people will criticize me for asking this potentially inappropriate question here, but I guess that the community here is quite unique in the ability of potentially answering my ...
3
votes
0answers
39 views

When is Fun(X,C) comonadic over C with respect to the colimit functor?

Because I'm primarily interested in this question from the point of view of $\infty$-categories (in this case, modeled by quasicategories), I'll ask this question using that terminology. In particular,...
0
votes
0answers
27 views

Sub-Gaussian decay of the measure of Euclidean balls

Let $X$ be a random vector in $\mathbb{R}^d$ satisfying the following property: there exists $C_1,C_2>0$ such that $$\int_0^{+\infty}\mathbb{P}(\|X-\mu_0\|\leq\sqrt{t})\exp(-t)dt\leq C_1\exp(-C_2\|\...
-2
votes
0answers
35 views

How can I solve this issue?

I have a problem related to this theme system analysis and action research. If you can please solve this, in another case please take me more resource for understanding this. The system consists of N-...
4
votes
0answers
84 views

Greatest prime factor of n and n+1

For a positive integer $n$ we denote its largest prime factor by $\operatorname{gpf}(n)$. Let's call a pair of distinct primes $(p,q)$ $\textbf{nice}$ if there are no natural numbers $n$ such that $\...
-6
votes
1answer
52 views

HTTP GET request in math [on hold]

How would I go about making an HTTP GET request? I've tried looking at Curl for math, but it just doesn't provide enough information. Can I do something like this? $d = g([S,O,M,E,U,R,L])$ Thanks.
1
vote
0answers
57 views

The cobordism hypothesis, and the bordism n-category as a free construction

In this question, I write $\text{Bord}_n$ for the symmetric monoidal $n$-category of framed n-bordisms, and $\text{D}_n$ for the free symmetric monoidal $n$-category with all duals on the terminal ...
0
votes
0answers
23 views

Holomorphic maps from upper half plane to itself (or equivalently Poincare disc to itself)

Suppose I parametrize complex plane by coordinates,$$z = x+i y,\ \bar z=x-i y$$ then the upper half plane, $\mathbb H_+$ is given by $y>0$. I am looking for chiral coordinate transformations, $f(z)$...
2
votes
1answer
37 views

Projection of an invariant almost complex structure to a non-integrable one

My apologies in advance if my question is obvious or elementary. We identify elements of $S^3$ with their quaternion representation $x_1 + x_2i + x_3j + x_4k$. We consider two independent vector ...

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