Revision as of 19:38, 21 April 2025 by Bot (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div> {{Alert-warning|This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion. }}Futher advance in your understanding of <math>S_N\to S_N^+</math>, as follows: <ul><li> Prove that <math>S_3^+=S_3</math>, by using a clever method, of your choice. </li> <li> Prove that <math>S_4^+\neq S_4</math>, a...")
BBot
Apr 21'25
Exercise
[math]
\newcommand{\mathds}{\mathbb}[/math]
This article was automatically generated from a tex file and may contain conversion errors. If permitted, you may login and edit this article to improve the conversion.
Futher advance in your understanding of [math]S_N\to S_N^+[/math], as follows:
- Prove that [math]S_3^+=S_3[/math], by using a clever method, of your choice.
- Prove that [math]S_4^+\neq S_4[/math], again by using a clever method, of your choice.
- Prove that [math]S_4^+[/math] is coamenable, while [math]S_5^+[/math] is not coamenable.
- Can we talk about quantum permutations of finite quantum spaces?
- If yes, can you prove that for [math]M_2[/math], given by [math]C(M_2)=M_2(\mathbb C)[/math], we get [math]SO_3[/math]?
- Based on this, can we say that [math]S_4^+[/math] should be a kind of twist of [math]SO_3[/math]?