What are the prerequisites for studying Lie theory and which books should I use?

Saussy
Messages
3
Reaction score
0
I have been working on getting the necessary mathematical education to start working on more advanced physics. The need for Lie theory has come up. I already know topology and differential geometry. Are there any other prerequisites to begin studying Lie theory? What books should I look into for the prerequisites and Lie theory itself?
 
Mathematics news on Phys.org
Hi Saussy! :smile:

I've got two excellent references for you:
  • Introduction to Smooth Manifolds by Lee. Fine, this is a differential geometry book, but it has quite a few material on Lee groups and stuff. It won't be comprehensive, but it's certainly worth a look.
  • Matrix groups by Baker: you won't need too much differential geometry for this one. Knowing the basic notions is good enough. It also deals a lot with linear algebra and matrices. But it's an excellent reference for Lie groups and Lie algebra's as well!
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.

Similar threads

Replies
2
Views
3K
Replies
5
Views
2K
Replies
2
Views
2K
Replies
1
Views
2K
Replies
9
Views
2K
Replies
38
Views
4K
Back
Top