Cohomologie des algèbres de Lie croisées et K-théorie de Milnor additive
Annales de l'Institut Fourier, Tome 45 (1995) no. 1, pp. 93-118.

Dans cet article, nous définissons des modules de (co)-homologie ℌ0(𝔊,𝔄), ℌ1(𝔊,𝔄), ℌ∘(𝔊, 𝔄), ℌ1(𝔊,𝔄) où 𝔊 et 𝔄 sont des algèbres de Lie munies d’une structure supplémentaire (algèbres de Lie croisées), qui satisfont les propriétés usuelles des foncteurs cohomologiques. Si A est une k-algèbre, nous utilisons ces modules d’homologie pour comparer le groupe d’homologie cyclique HC1(A) avec un analogue additif du groupe de K-théorie de Milnor K2Madd(A).

In this paper we define modules of (co)-homology ℌ0(𝔊,𝔄), ℌ1(𝔊,𝔄), ℌ∘(𝔊,𝔄), ℌ1(𝔊,𝔄) where 𝔊 and 𝔄 are Lie algebras with an extra structure (crossed Lie algebras). This modules satisfy the usual properties of cohomological functors, in particular existence of an exact sequence associated to a short exact sequence of coefficients.

For a k-algebra A, equipped with the trivial Lie algebra structure, we use these homology modules to compare the cyclic homology groupe HC1(A) with an additive analogue of the Milnor’s group K2Madd(A).

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Guin, Daniel. Cohomologie des algèbres de Lie croisées et $K$-théorie de Milnor additive. Annales de l'Institut Fourier, Tome 45 (1995) no. 1, pp. 93-118. doi : 10.5802/aif.1449. https://www.numdam.org/articles/10.5802/aif.1449/

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