# Properties

 Label 6.2.B.d36 Name $$\mathrm{U}(1)[D_{36}]$$ Weight $6$ Degree $2$ Real dimension $1$ Components $72$ Contained in $$\mathrm{U}(2)$$ Identity component $$\mathrm{U}(1)$$ Component group $$D_{36}$$

# Learn more about

## Invariants

 Weight: $6$ Degree: $2$ $\mathbb{R}$-dimension: $1$ Components: $72$ Contained in: $\mathrm{U}(2)$ Rational: no

## Identity component

 Name: $\mathrm{U}(1)$ Index: $72$ $\mathbb{R}$-dimension: $1$ Description: $\left\{\begin{bmatrix}\alpha&0\\0&\bar\alpha\end{bmatrix}:\alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\}$ Symplectic form: $\begin{bmatrix}0&1\\-1&0\end{bmatrix}$ Hodge circle: $u\mapsto \mathrm{diag}(u,u^{-1})$

## Component group

 Name: $D_{36}$ Order: $72$ Abelian: no Generators: $\left\{\begin{bmatrix} 0 & 1\\ -1 & 0\end{bmatrix}, \begin{bmatrix} 1 & 0 \\ 0 & \zeta_{36}\end{bmatrix}\right\}$

## Moment sequences

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