论文标题
在环形环上的单一组的商图和汞合金演示
Quotient graphs and amalgam presentations for unitary groups over cyclotomic rings
论文作者
论文摘要
假设$ 4 | n $，$ n \ geq 8 $，$ f = f_n = \ mathbb {q}（ζ_n+\barζ_n）$，并且有一个Prime $ \ Mathfrak {p} = \ Mathfrak {p} _n $ in $ f_n $中的$ 2 $ in $ f_n $中的$ 2 $。我们研究了$ \ peripatorName {pu_ {2}}（\ Mathbb {Z} [ζ_N，1/2]）$和$ \ operatorName {psu_ {2}}（\ m mathbb {z} [z____n，1/2]）$ clifford-cycycycy的amalgam演示。这些汞齐来自这些组在bruhat-tits树上的动作，$δ=δ_ {\ mathfrak {\ mathfrak {p}} $ for $ \ operatatorName {sl_ {2}}}（f_ \ mathfrak {p}）$是通过Hamilton Quaternions构建的。 We explicitly compute the finite quotient graphs and the resulting amalgams for $8\leq n\leq 48$, $n\neq 44$, as well as for $\operatorname{PU_{2}}(\mathbb{Z}[ζ_{60}, 1/2])$.
Suppose $4|n$, $n\geq 8$, $F=F_n=\mathbb{Q}(ζ_n+\barζ_n)$, and there is one prime $\mathfrak{p}=\mathfrak{p}_n$ above $2$ in $F_n$. We study amalgam presentations for $\operatorname{PU_{2}}(\mathbb{Z}[ζ_n, 1/2])$ and $\operatorname{PSU_{2}}(\mathbb{Z}[ζ_n, 1/2])$ with the Clifford-cyclotomic group in quantum computing as a subgroup. These amalgams arise from an action of these groups on the Bruhat-Tits tree $Δ=Δ_{\mathfrak{p}}$ for $\operatorname{SL_{2}}(F_\mathfrak{p})$ constructed via the Hamilton quaternions. We explicitly compute the finite quotient graphs and the resulting amalgams for $8\leq n\leq 48$, $n\neq 44$, as well as for $\operatorname{PU_{2}}(\mathbb{Z}[ζ_{60}, 1/2])$.
