Hello! Can someone please explain to me the concept behind the adjoint representation of a Lie group? I have run through the theory but I ma not quite getting it.
In my book the author gives such definition
''Take any and define homomorphism by conjugation
This homomorphism is called the adjoint representation of G''
What does it do?
I have also noticed that there is also an adjoint representation of a Lie algebra? what is the difference?
Yes I am an undergraduate student so I am mostly asking about basic things
We use quite advanced book ''Topology, geometry and physics'' of Nakahara. His book is quite difficult because it is directed to graduated students and requires very much mathematical preliminaries (which undergraduate students quite ofthe dont have)
I have an idea what the adjoint representation might be but I have problems with some physical interpretation of it which is most important in this case.
Writting just a definition and some formulae does not help with understanding the whole concept behind it at all. It just makes it boring for the reader. It is always very helpful to try to interpret physically and give examples.
You are right, I do not need the definition. I need rather some help to interpret the definition. By saying what does it do I wonder what can this be good for, where we can use it, how this representations apply to Lie groups and so on so when I present it to the other students I can give them something better than just 'dry' boring definition which not everyone might understand it.
Your last sentence is precisely what I am after, but I think you are describing the adjoint representation of Lie algebras- not Lie groups???