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Results tagged with lie-algebras
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user 4008
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
votes
Resolution of a free lie algebra as a module over its universal enveloping algebra.
There is a very small resolution. Everything is graded so we can in fact speak
of minimal resolutions. The most refined version is to make the basis (which I
for simplicity assume is finite of cardina …
- 22.6k
3
votes
Accepted
Is there an analog of Clifford Theorem in the setting of Lie algebras?
The positive results seem at most to be tied to finite dimensional representations in positive characteristic:
Let $\frak H$ be the Heisenberg algebra with basis $x,y,$ where $c$ is central and $[y,x …
- 22.6k
6
votes
Accepted
What is the universal enveloping algebra?
I have now understood the situation better so my previous post has been replaced
by this. (The only thing that was in the original but will not be here are some
explicit formulas but Theo has given a …
- 22.6k
12
votes
Torsion for Lie algebras and Lie groups
I don't know the answer to the actual question but here is a situation which
should be similar but simpler. Consider an integral polynomial group law $G$,
i.e., a group scheme structure on the affine …
- 22.6k
22
votes
What algebraic group does Tannaka-Krein reconstruct when fed the category of modules of a no...
After some thought my pessimism (as expressed in my concurrence with the answer
of Milne) has abated somewhat. If I were bold enough I would conjecture the
following (assuming that the characteristic …
- 22.6k
4
votes
Accepted
Restricted universal enveloping algebra of Abelian p-Lie algebra
I don't think so. Consider the case which should be the most difficult to split canonically, the case when the $p$'th power map is zero. The automorphism group is then equal to the linear automorphism …
- 22.6k
14
votes
What is a "block" in an abelian category?
It seems clear to me that blocks should have something to do with the
decomposition of the category as a direct product of subcategories. A
decomposition into a product of two factors corresponds exac …
- 22.6k