The discussion revolves around the adjoint representation of the special unitary group SU(2), specifically focusing on the relationship between the adjoint and coadjoint actions, as well as the computation of matrix exponentials related to these representations.
Participants are actively engaging with the problem, sharing resources and insights. Some guidance has been offered regarding the complexity of matrix exponentiation and the potential for mistakes with larger matrices. There is an acknowledgment of the need for clarity in the calculations being performed.
There is mention of specific resources and prior articles that may contain relevant information, as well as the challenges posed by the calculations involving matrix exponentials of different sizes.
It's not really funny to calculate the exponentials of ##(3\times 3)-##matrices and easy to make mistakes. I guess, that's why I haven't really seen it anywhere. I would start with ##(2\times 2)-##matrices and the Lie group of matrices of the form ##\begin{bmatrix}a&b\\0&0\end{bmatrix}## with ##a \neq 0## and the Lie algebra ##[X,Y]=Y## which is easier than with simple Lie groups which have entries on both sides of the diagonal. It's also the reason why I used the differentiation of curves in the Lie group to show the connection to its Lie algebra. Exponentiation is basically the way back, an integration.nigelscott said:When I try to calculate the matrix exponential I get strange results. Any pointers you could give would be of great help.