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Results tagged with lie-algebras
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user 7108
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
votes
Which is the correct universal enveloping algebra in positive characteristic?
This question popped up on the feed recently, and I wanted to add another, "brave new math"-style answer. Namely, the point of Lie algebras is that, in characteristic $0$, a Lie algebra (resp., an $L_ …
- 7,952
4
votes
1
answer
532
views
Can a simple lie algebra be determined by weights of its representation?
Suppose you are given a linear combination of points of $\mathbb{Z}^n$ which corresponds to the weight datum of a nontrivial representation $V$ of some simple Lie algebra $g$. Is it possible to recons …
- 7,952
0
votes
Accepted
Can a simple lie algebra be determined by weights of its representation?
I'll write this as an answer rather than a comment to close the question. Victor Protsak's comment gives the original question a definitive answer of no.
The formulation of the original question is …
- 7,952