Recent content by N1k1tA

Why is the group of orthochronous proper Lorentz transformations connected?

I've decided to work on some topics about supersymmetry for my undergraduate thesis. My background is that I have had a one-semester course in differentiable manifolds, plus typical undergrad math courses, real analysis and module theory (graduate algebra). So, I went to the library and found a...

##S^3## is the ##3##-sphere (the ##3##-dimensional sphere embedded in ##\mathbb{R}^4##), while ##S_3## is the group of permutations on ##3## letters. Totally different things. Does your problem concern Lie groups or any arbitrary groups?

Yes, there are many such examples. if I'm not mistaken ##\mathrm{Aut}(S_n)=S_n## for all ##n## except ##2,6##. But you can check it by hand that ##\mathrm{Aut}(S_3)=S_3##. The groups with this property are called complete groups.