Euclidian and Hyperbolic rotations

neerajareen
Messages
17
Reaction score
0
Do hyperbolic rotations of euclidian space and ordinary rotations of euclidian space form a group?
 
Physics news on Phys.org
Yes, the ordinary rotations form a group called ##SO(n)##. The hyperbolic rotations also form a group, that's apparently called ##SO^+(1,1)##.
 
No I meant, can they form a group together. Can they be put in the same group? Just like how Lorentz boosts and rotations are combined into the Lorentz group?
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Do hyperbolic harmonics exist?
Replies
1
Views
3K
I Finding the orthogonal projection of a vector without an orthogonal basis
Replies
3
Views
4K
A The colorful world of ##2\times 2## complex matrices
Replies
7
Views
2K
I Lie Algebra states of a representation
Replies
5
Views
2K
I Clock rate in hyperbolic space-time manifold
Replies
1
Views
854
I Did Born Rigidity Lead Einstein to Conclude Spacetime is Curved?
Replies
5
Views
2K
MHB Need help understanding a Lie Algebra
Replies
7
Views
2K
A In What Space Does Quantum Spin Take Place
Replies
10
Views
2K
I Outer product in geometric algebra
Replies
8
Views
3K
What Are the Fascinating Rotations of 3-Spheres in 4D Space?
Replies
13
Views
3K

Hot Threads

Recent Insights

Back
Top