⧼exchistory⧽
5 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Prove that we have [math]S_3=S_3^+[/math] by looking at the coaction
[[math]]
\Phi:\mathbb C^3\to\mathbb C^3\otimes C(S_3^+)
[[/math]]
written in terms of the Fourier basis of [math]\mathbb C^3[/math].
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Prove directly, without Kesten, that the discrete quantum group
[[math]]
\Gamma=\widehat{S_5^+}
[[/math]]
is not amenable, in the discrete quantum group sense.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Consider a discrete group generated by elements of finite order, written as a quotient group, as follows:
[[math]]
\mathbb Z_{N_1}*\ldots*\mathbb Z_{N_k}\to\Gamma
[[/math]]
Prove that we have an embedding [math]\widehat{\Gamma}\subset S_N^+[/math], where [math]N=N_1+\ldots+N_k[/math].
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Prove that we have the following equality:
[[math]]
S_{M_2}^+=SO_3
[[/math]]
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Check out all the details for Theorem 9.22, regarding the Poisson and free Poisson limiting theorems.