Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with homological-algebra
Search options not deleted
user 4231
(Co)chain complexes, abelian Categories, (pre)sheaves, (co)homology in various (possibly highly generalized) settings, spectra, derived functors, resolutions, spectral sequences, homotopy categories. Chain complexes in an abelian category form the heart of homological algebra.
3
votes
The cohomology group $H^{1}(GL_{2}(\mathbb{F}_{p}), M_{2}(\mathbb{F}_{p}))$
There are really two questions here: (1) What is the dimension of this cohomology? (2) How do I compute it? Though it may not be strictly necessary, it's probably best to treat the cases $p=2$ and …
- 52.9k
13
votes
Accepted
Can the Jacobi-Trudi identity be understood as a BGG resolution?
Look at the short paper MR902299 (89a:17012) 17B10 (20C30)
Zelevinski˘ı, A.V. [Zelevinsky, Andrei] (2-AOS-CY),
Resolutions, dual pairs and character formulas. (Russian)
Funktsional. Anal. i Prilozhen. …
- 52.9k
7
votes
Confusion about Subcategories of Category $\mathcal{O}$
EDIT: To compensate for my attempted answer, which mainly added further confusion, I'll substitute the following remarks.
Note especially that on the algebraic side the confusion starts in the wordin …
- 52.9k
10
votes
1
answer
828
views
Is there a "correct" general setting for the principle: "tensoring any object with a projec...
Apparently this principle was first formulated for left modules over the group algebra $A=kG$ of a finite group, where $k$ is a field of characteristic $p>0$ dividing $|G|$. (See Exercise 2 on p. 426 …
- 52.9k
7
votes
Whitehead lemmas in Lie algebra cohomology for non-algebraically closed fields
There is no problem about the Whitehead lemmas over an arbitrary field of characteristic 0 in the context of (1) complete reducibility of finite dimensional representations of a semisimple Lie algebr …
- 52.9k
3
votes
Accepted
Complexity of rational $\mathrm{GL}_{n(r)}$-modules
I don't recall seeing an explicit answer to your question in the literature, but the basic outline starts with the (restricted) Lie algebra or first Frobenius kernel: here an upper bound on the comple …
- 52.9k
1
vote
Accepted
Coinduced modules in the BGG category $\mathcal O$ over complex semisimple Lie algebras
This line of questioning has been pursued in greater generality. starting in prime characteristic by Ron Irving (and myself) and then in the analogous setting of category $\mathcal{O}$ for a semisimpl …
- 52.9k
13
votes
4
answers
3k
views
What is a "block" in an abelian category?
In the literature and in some posts here, there has been variation in the undefined use of the term "block" for a category of modules over a ring, or more abstractly an abelian category (all of which …
- 52.9k