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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.

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 …
Matthieu Romagny's user avatar
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I have now understood the situation better so my previous post has been replaced by this.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 …
David White's user avatar
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3 votes
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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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar
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 …
Torsten Ekedahl's user avatar