终边在一、三象限角平分线的角的集合是 （  ）

A：$\left\{\alpha |\alpha =2k\mathrm{\pi }+\frac{\mathrm{\pi }}{4},\mathrm{k}\in \mathrm{Z}\right\}$

B：$\left\{\alpha |\alpha =k\mathrm{\pi }+\frac{\mathrm{\pi }}{2},\mathrm{k}\in \mathrm{Z}\right\}$

C：$\left\{\alpha |\alpha =2k\mathrm{\pi }+\frac{\mathrm{\pi }}{2},\mathrm{k}\in \mathrm{Z}\right\}$

D：$\left\{\alpha |\alpha =k\mathrm{\pi }+\frac{\mathrm{\pi }}{4},\mathrm{k}\in \mathrm{Z}\right\}$