The catenarity of the positive part of the quantized enveloping algebra of a simple Lie algebra of type . (La caténarité de la partie positive de l'algèbre enveloppante quantifiée de l'algèbre de Lie simple de type .)
We show that some iterated Ore extensions have the same behaviour with respect to injective resolutions as Gorenstein commutative rings.
We give axiomatic conditions in order to calculate the local cohomology of some idempotent kernel functors. These results lie in some new dimension introduced by T. Levasseur for Auslander-Gorenstein rings. Under some hypothesis, we generalize previous results.
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