So(3) Definition and 56 Threads

I was wondering if anyone can help me to show that the subset of SO(3) contaning all matrices A with det(A+id)=0 is a submanifold diffeomorphic to real projective plane. Thanks.

Hi! This is my first post here. I'm currently studying analytical/classical mechanics and have some problems understanding how the Lie algebra is formed in relation to the SO(3) group of rotations. My problem is this: Given a matrix representation R of some rotation around a fixed axis, we...

Hi all, I asked this on the Quantum Physics board but didn't get a response. I'm reading Cahn's book on semi-simple lie algebras and their representations. http://www-physics.lbl.gov/~rncahn/book.html In chapter 1, he attempts to build a (2j+1)-dimensional representation T of the Lie...

What's the correct way to state the relationship between these two Lie groups? One is the "covering group" of the other, right? Okay, then - what's that mean, to a non-expert? I know the basics, i.e. SO(3) can be represented by rotation matrices in 3-space, and U(2) does the same in a...

1) Let P,Q be planes through the origin in R3. Let Rp, Rq be the corresponding reflections. Is Rp*Rq (where * denotes "composition") in SO(3) or O(3)/SO(3)? What is the axis of rotation of Rp*Rq? 2) For a fixed A in SO(3) show that there are infinitely many pairs of planes P,Q such that...

group theory : orbits hi. I'm trying to calculate the orbits of some simple groups. I have found many explanations of what they are, but no example calculations. does anyone have any ideas where to look. I'm trying to calculate the orbit of SO(3). thanks