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Results tagged with lie-algebras
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user 50929
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.
6
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1
answer
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Does the centralizer of a regular element in a semisimple Lie algebra act by polynomials?
Let $\mathfrak g$ be a semisimple Lie algebra over $\mathbb C$, $\rho : \mathfrak g \to \operatorname{End}(V)$ a finite-dimensional irreducible representation and $x \in \mathfrak g$ regular with cent …
- 348
6
votes
Accepted
Does the centralizer of a regular element in a semisimple Lie algebra act by polynomials?
It is false for the same reason the first example is wrong. Take $\rho$ for example the adjoint representation. As soon as $\mathfrak g$ has rank at least $2$ you can find a regular semisimple $x$ suc …
- 348