Lie Groups and Lie Algebras Flashcards
1
Q
What does it mean for a group to be Abelian?
A
It is commutative
2
Q
What is U(1)
A
Unitary 1x1 matrices
3
Q
What is SU(2)
A
Unitary 2x2 matrices with det 1
4
Q
What is the exponential as a limit
A
5
Q
What shape is SU(2)
A
3 sphere
6
Q
What are the Pauli matrices
A
7
Q
Give the commutator and anti commutator relations of the Pauli matrices
A
8
Q
What can any element of SU(2) be written as
A
9
Q
Define a topological space
A
10
Q
Define a homeomorphism
A
11
Q
Define Hausdorff
A
12
Q
Define a differentiable manifold
A
13
Q
What is a path?
A
14
Q
What is a tangent vector?
A
15
Q
What is the tangent space?
A
16
Q
What is a Lie group?
A
17
Q
What is a lie algebra
A
18
Q
When are combination of a lie algebra and lie group in the algebra/group
A
19
Q
Define compactness
A
20
Q
When is the exponential map surjective?
A
