Intereting Posts

Compact operator on $l^2$
How to show that remainder $\beta X \setminus \beta(X)$ is an $F_\sigma$-set in $\beta X$.
Solutions to $ax^2 + by^2 = cz^2$
Three points on a circle
Show that $\mathbb{R}^{\mathbb{R}} = U_{e} \oplus U_{o}$
Analogy between linear basis and prime factoring
Equivalence of Archimedian Fields Properties
A (non-artificial) example of a ring without maximal ideals
Limit of sequence of sets – Some paradoxical facts
What is the importance of the infinitesimal generator of Brownian motion?
Multi variable integral : $\int_0^1 \int_\sqrt{y}^1 \sqrt{x^3+1} \, dx \, dy$
Prove that the maximum value of $|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2$ is $9$
Showing that $\Omega$ is of class $C^1$
Presentation of group equal to trivial group
Proof that sum of first $n$ cubes is always a perfect square

Often I have heard about the link between Algebra (in particular Representations of Groups and Algebras) and some “indefinite” field of Physics.

I have a good preparation in Algebra and Representation Theory (in particular about Representations of Lie Algebras), and I’m fascinated with Physics. My idea is try to understand this link and eventually study it with more depth.

Hence I’m looking for an introductory book that emphasizes the applications of Algebra in Physics from a comprehensible and mathematical point of view.

- Structure constants for and the adjoint representation and meaning in $sl(2,F)$
- Lie Groups/Lie algebras to algebraic groups
- Normal Subgroups of $SU(n)$
- Lie algebra of a quotient of Lie groups
- To what extent are the Jordan-Chevalley and Levi Decompositions compatible.
- Reference for Lie-algebra valued differential forms

Does anyone have an idea for a book with these requisites?

Thank you!

- How to draw a weight diagram?
- Mathematical background for TQFT
- Reference for Lie-algebra valued differential forms
- Gentle introduction to fibre bundles and gauge connections
- Why does the “separation of variables” method for DEs work?
- What exactly are pseudovectors and pseudoscalars? And where could I read about them?
- Relation between root systems and representations of complex semisimple Lie algebras
- Finding the basis of $\mathfrak{so}(2,2)$ (Lie-Algebra of $SO(2,2)$)
- Symplectic group action
- Parameters on $SU(4)$ and $SU(2)$

Howard Georgi’s “Lie Algebras in Particle Physics” is good, if more intended for the physicist going towards the math than vice versa. It should provide a lot of context, though, and there’s a PDF version floating around on google. I’d say similar things about these two introductions to aspects of high-energy theory [1] [2].

I’ll see if I can remember some other good ones.

Peter Woit, the author of the book “Not Even Wrong” and a blog by the same name, has been working on a book on quantum mechanics as described by representation theory. The latest draft may be found at the following link:

Quantum Theory, Groups and Representations:

An Introduction.

- Is my proof that the product of covering spaces is a covering space correct?
- What's the dual of a binary operation?
- Set Theory – Subset of set
- Proving pointwise convergence of series of functions
- Sheaves and complex analysis
- Number of zeroes at end of factorial
- How do you divide a polynomial by a binomial of the form $ax^2+b$, where $a$ and $b$ are greater than one?
- Laurent-series expansion of $1/(e^z-1)$
- What are the issues in modern set theory?
- $S^{-1}A \cong A/(1-ax)$
- Categorical generalization of intersection?
- How to prove that every real number is the limit of a convergent sequence of rational numbers?
- Prove that $\gcd(e,f)=1$.
- Explanation for summation complex analysis method
- Deduction of usual Cayley-Hamilton Theorem from “Determinant Trick”