The distinct affine algebraic groups
$$
SL_2(\mathbb C)
\quad\text{and}\quad
PGL_2(\mathbb C)=SL_2(\mathbb C)/\{\pm I\}
$$
both have the <Special linear Lie algebra> $\mathfrak{sl}_2(\mathbb C)$. Quotienting a <Lie group> by a discrete central subgroup does not change its tangent Lie algebra.

Solution

Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 102 / 1 / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-102/1/ii/solution