# Tagged Questions

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### Where does the name “toral” come from?

Where does the name "toral" come from in "toral subalgebra"? I know a little (very little) Lie groups theory, so I guess it could be related to a Lie group whose Lie algebra is the toral one. Is ...
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### Why are “restricted Lie algebras” called restricted?

Restricted Lie algebras are Lie algebras of characteristic $p$ with an additional unary operation which is like raising to $p$th power. I didn't find any motivation for this strange choice of the name ...
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### What does boson-type realization mean?

I have seen several different contexts the expression "boson-type realization", for instance in the study of algebras growth and realization of affine algebras. To be or not be a boson-type ...
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### Usage and determination of “rank” and “dimension” of groups & representations

Physicist here. I seem to see conflicting statements about the rank of some groups I've come across lately. A paper I'm reading states that $SO(6)$ is rank 3 and therefore its Cartan subalgebra ...
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### preserves eigen spaces?

"Let $H_0=\begin{pmatrix}i&0\\0&-i\end{pmatrix}$, suppose $A\in SU(2)$ commutes with $H_0$, it must preserves each eigen spaces for $H_0$, eigen spaces for $H_0$ are just $\mathbb{C}e_1$ and ...
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### Understanding the Lie algebra $o_{V,B}$

I am learning about Lie algebras and I do not understand the following subalgebra of $\mathfrak gl_{V}$. Let $V$ be a vector space and $\mathfrak gl_{V}$ be the Lie algebra of endomorphisms on $V$. ...
I am currently working on the topic of Lie - Algebras and I have stumbled a few times over the expression "direct summand in a tensor product". The text says that $\ V(\lambda)$ as an ...