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Results tagged with homological-algebra
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user 32332
(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.
5
votes
Accepted
On Serre's problem regarding the injectivity of Albert-Algebra cohomological invariants
In the lecture notes Albert algebras by H.P. Petersson, written in $2012$ this is still mentioned as an open problem, see Question $13.2$:
Is an Albert algebra $J$ determined up to isomorphism by its …
- 12.1k
4
votes
Accepted
"as close to being semisimple as it can possibly be."
In the semisimple case it is really easy to calculate $ext_A^i(M,N)$, $i\ge 1$, with the above assumptions. It is zero. For Koszul rings this is almost
true, i.e., $ext^i(M,N)$ is concentrated in degr …
- 12.1k
6
votes
Poincaré duality for (co)homology of Lie algebras?
As far as I know, a generalisation of Poincare duality for Lie algebra cohomology over rings is given in
M. Hazewinkel, "A duality theorem for the cohomology of Lie algebras" Math. USSR-Sb. , 12 (19 …
- 12.1k