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Results tagged with lie-algebras
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user 41139
Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
15
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What is the relation between spherical principal series representations of a reductive Liegr...
Here is an issue that thoroughly confuses me. I hope I can express it in a way that is clear cut enough for this site.
Let $G$ be a real reductive Lie group and $\mathfrak{g}$ be the complexification …
- 2,493
4
votes
Is the triple product in a Freudenthal triple system fully symmetric?
I figured out the precise relationship between the 'Class of Ternary Algebras' of Faulkner and the 'Freudenthal Triple Systems' of Ferrar/Helenius and I will write it down here for the benefit of futu …
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6
votes
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Is the triple product in a Freudenthal triple system fully symmetric?
I'm trying to learn about Freudenthal triple systems. Here is the definition given by Helenius [1], start of Section 5:
A Freudenthal triple system is a finite-dimensional vector space $V$
over …
- 2,493
14
votes
3
answers
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Where does the really nice '8-dimensional' description of the $E_7$ root system come from?
The Wikipedia page on $E_7$ tells me:
Even though the roots span a 7-dimensional space, it is more symmetric and convenient to represent them as vectors lying in a 7-dimensional subspace of an 8-d …
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7
votes
Accepted
First Explicit Irreducible Representations
I think "Group Theory for Unified Model Building" by R. Slansky qualifies. As the title suggests it is written with an application in physics (beyond my understanding) in mind, but the tables are very …
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3
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The Casimir invariant of an irreducible representation of a compact Lie group
[I started to type this as a comment but it took like ten comments to fit, so I paste it into an answer. It is an answer as it explains how you can use the references you already have to answer your q …
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