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Results tagged with lie-algebras
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user 17660
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.
5
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Finite dimensional homogeneous spaces of $Diff(S^1)$
This question is a refined version of Representations of infinite dimensional Lie algebras as vector fields on manifolds
I'm interested in the finite dimensional homogeneous spaces of $Diff(S^1)$. Th …
- 548
5
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answer
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Representations of infinite dimensional Lie algebras as vector fields on manifolds
Suppose I have e.g. the Witt algebra,
$\left[l_n,l_m \right] = -(n-m)l_{n+m}$.
I want to realize the $l_n$ as vector fields on some manifold. The classical example is when the $l_n$ span the Lie a …
- 548
5
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Why the Gell-Mann matrices in the SU(3)-model need to be trace orthogonal ?
It's just a choice of a basis. Compare it to an orthogonal vector basis. And please... try to write math in LaTeX :) (see the "How to write math" box on the right and below).
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How to find Casimir operators?
I'm assuming you're thinking of some specific matrix representation $X_i \in \mathfrak{g}$ (let's assume it's the defining representation). Compute the Killing form, $\kappa_{ij} \doteq Tr (X_i\cdot X …
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