The generator of the analytic group with its Lie algebra $g=rad(g)oplus sl(2,F)$

摘要

The purpose of thes paper is to find the generator of the analytic group with its Lie algebra $rak g={ext{ rad}}(rak g) oplus rak{sl} (2, Bbb F)$, where $Bbb F$ is $Bbb R$ or $Bbb C$ (Theorem 3. 1). An analytic group means a connected Lie group. To obtain this purpose, we first find the generator of $SL(2, Bbb F)$ (Corollary 1.3) and the generator of an analytic group with Lie algebra $sl(2, Bbb F)$ (Proposition 1.4).