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Results tagged with lie-algebras
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user 22989
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.
12
votes
Is a retract of a free object free?
A few months after the last activity on this question, Neena Gupta gave a proof that over a field $k$ of positive characteristic, a retract of a polynomial algebra need not be a polynomial algebra: ht …
- 35.2k
5
votes
Accepted
Infinite Krull-Schmidt categories?
The statement about simple Lie algebras is not true.
A (finitely generated right) module $P$ for a ring $R$ is stably free if $P\oplus R^m\cong R^n$ for some integers $m,n$.
Suppose $R$ has a non-f …
- 35.2k
17
votes
Accepted
Tilting Objects in BGG Categories $\mathcal{O}$
Words change their meanings.
The original meaning of “tilting module” is that of Happel and Ringel in the representation theory of finite dimensional algebras, which requires the projective dimension …
- 35.2k
6
votes
A Hom-Tensor identity - $\text{Hom}_{R}(P,B)\otimes _SC \cong \text{Hom}_{R}(P,B \otimes_S C) $
Fix a finitely generated left $R$-module $_RP$ that is in $\mathcal{C}$ and projective as an object of $\mathcal{C}$, and a finite dimensional left $S$-module $_SC$.
As noted in the question, for any …
- 35.2k