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Results tagged with homology
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user 345
Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
3
votes
Homology of solvable (nilpotent) Lie algebras
This can be computed as $\mathrm{Tor}_j^{U(\mathfrak{g})}(U(\mathfrak{g})/(z), \mathbb{C}_\lambda)$ which is the $j$th homology group of $$0\to U(\mathfrak{g})\otimes_{U(\mathfrak{g})} \mathbb{C}_\lambda …
- 3,545
3
votes
Homology of solvable (nilpotent) Lie algebras
In particular if $V_S=0$ then all homology groups of $V$ are trivial.
Now we come to the paper of Ken Brown numdam.org/article/CM_1984__53_3_347_0.pdf I mentioned in the comments. … So we see that this sufficient condition for vanishing homology is not necessary but gets you somewhere. …
- 3,545