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4 exercise(s) shown, 0 hidden
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Compute the quantum isometry groups of the twisted polygonal spheres, which are by definition given by
[[math]]
C(\bar{S}^{N-1,d-1}_\mathbb R)=C(\bar{S}^{N-1}_\mathbb R)\Big/\Big \lt x_{i_0}\ldots x_{i_d}=0,\forall i_0,\ldots,i_d\ {\rm distinct}\Big \gt
[[/math]]
at the missing values of the parameter, [math]d=3,4,\ldots,N-1[/math].
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Work out the full theory of the quantum group [math]H_N^{[\infty]}[/math], notably with a Brauer type result for it, and then with probability computations.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Work out the full theory of the quantum group [math]K_N^{[\infty]}[/math], notably with a Brauer type result for it, and then with probability computations.
BBot
Apr 22'25
[math]
\newcommand{\mathds}{\mathbb}[/math]
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Find suitable quantum group axioms covering the quantum isometry groups of the main polygonal spheres, namely
[[math]]
\xymatrix@R=12mm@C=17mm{
O_N\ar[r]&O_N^*\ar[r]&O_N^+\\
H_N\ar[r]\ar[u]&H_N^{[\infty]}\ar[r]\ar[u]&\bar{O}_N^*\ar[u]\\
H_N^+\ar[r]\ar[u]&H_N\ar[r]\ar[u]&\bar{O}_N\ar[u]}
[[/math]]
and then do the same in the complex case.