1. ### I What do we mean when we say something transforms "under"...

What do we mean when we are talking about something that transforms under a representation of a group? Take for example a spinor. What is meant by: this two component spinor transforms under the left handed representation of the Lorentz group? When we talk about something that transforms...
2. ### Other Using Michael Artin's "Algebra" for Group Theory

Hi all, I have stumbled upon Artin's book "Algebra" and was wondering if I could use it to do some self-study on Group Theory. Some background: I am a physics undergraduate who has some competence in elementary logic, proofs and linear algebra. It seemed to me that ideas related to Group...
3. ### Sub groups of the dihedral group

Homework Statement This is only a step in a proof I am trying to make. Let Dm be the dihedral group. r is the rotation of 2π/m around the origin and s is a reflexion about a line passing trough a vertex and the origin. Let<s> and <r> be two subgroups of Dm. Is there a theorem that states...
4. L

### I How many generators can a cyclic group have by definition?

Hi, so I have just a small question about cyclic groups. Say I am trying to show that a group is cyclic. If I find that there is more than one element in that group that generates the whole group, is that fine? Essentially what I am asking is that can a cyclic group have more than one generator...
5. ### Show GL/O/SO(n,R) form groups under Matrix Multiplication

Homework Statement Show that the set GL(n, R) of invertible matrices forms a group under matrix multiplication. Show the same for the orthogonal group O(n, R) and the special orthogonal group SO(n, R). Homework Equations The Attempt at a Solution So I know the properties that define a group...
6. ### B Matrices of su(3) and sphere symmetry

i used to get pauli matrices by the following steps it uses the symmetry of a complex plane sphere i guess so..? however i cant get the 8 gell mann matrices please help !! method*: (x y) * (a b / c d ) = (x' y') use |x|^2 + |y|^2 = |x'|^2 + |y'|^2 and |x| = x * x(complex conjugate) this way...
7. ### Insights Groups and Geometry - Comments

micromass submitted a new PF Insights post Groups and Geometry Continue reading the Original PF Insights Post.
8. ### I Why only normal subgroup is used to obtain group quotient

Hello! As far as I know any subgroup can, in principle, be used to divide group into bundle of cosets. Then any group element belongs to one of the cosets (or to the subgroup itself). And such division still is not qualified as a quotient. Yes, the bundle of cosets in this case will be...
9. ### Determine if a group is cyclic

Hello all! If I have a group of order 20 that has three elements of order 4, can this group be cyclic? What if it has two elements? I am new to abstract algebra, so please keep that in mind! Thanks!
10. ### Tensor product and representations

Hi, I that <I|M|J>=M_{I}^{J} is just a way to define the elements of a matrix. But what is |I>M_{I}^{J}<J|=M ? I don't know how to calculate that because the normal multiplication for matrices don't seem to work. I'm reading a book where I think this is used to get a coordinate representation of...