5
votes
1answer
202 views

History of Lie algebra notation (in Fraktur)?

Does anyone know how it has become the standard to express Lie algebras in fraktur? I'd also like to know how it's established for each era and region, not only the origin. It doesn't seem that ...
5
votes
4answers
541 views

What does the symbol $\operatorname{Tr}$ in the Yang-Mills action mean?

I find that many authors write the Yang-Mills action as follows: $$\mathcal{J}= \int \operatorname{Tr}(F \wedge \star F).$$ I have yet to find a formal description of the symbol $\operatorname{Tr}$ ...
0
votes
1answer
179 views

What is meant by $\sum_{p + q = v + w} {\dim V_p * \dim W_q}$?

I am currently working on the topic of Lie - Algebras. What is meant by $\displaystyle\sum_{p + q = v + w} {\dim V_p * \dim W_q}$ ? $\ V_v $ and $\ W_w $ denote weight spaces I don't know how to ...
3
votes
1answer
564 views

Why do we use the commutator bracket for Lie algebra's

We define Lie algebras abstractly as algebras whose multiplication satisfies anti-commutativity and Jacobi's Identity. A particular instance of this is an associative algebra equipped with the ...