# Properties

 Label 2.2.3.c8 Name $$\mathrm{SU}(2)[C_{8}]$$ Weight $2$ Degree $2$ Real dimension $3$ Components $8$ Contained in $$\mathrm{O}(2)$$ Identity component $$\mathrm{SU}(2)$$ Component group $$C_8$$

## Invariants

 Weight: $2$ Degree: $2$ $\mathbb{R}$-dimension: $3$ Components: $8$ Contained in: $\mathrm{O}(2)$ Rational: yes

## Identity component

 Name: $\mathrm{SU}(2)$ $\mathbb{R}$-dimension: $3$ Description: $\left\{\begin{bmatrix}\alpha&\beta\\-\bar\beta&\bar\alpha\end{bmatrix}:\alpha\bar\alpha+\beta\bar\beta = 1,\ \alpha,\beta\in\mathbb{C}\right\}$ Symplectic form: $\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ Hodge circle: $u\mapsto\mathrm{diag}(u,\bar u)$

## Component group

 Name: $C_8$ Order: $8$ Abelian: yes Generators: $\begin{bmatrix}1&0\\0&\zeta_{8}\end{bmatrix}$

## Moment sequences

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $0$ $0$ $0$ $0$ $0$ $0$ $14$ $0$ $0$ $0$ $0$