Homological Algebra/Lie Algebras
Cartan homotopy formulae and the bivariant Hochschild complex
[Formule homotopique de Cartan et le complexe de Hochschild bivariant]

Présenté par : Alain Connes

Banerjee, Abhishek1
1 Department of Mathematics, Johns Hopkins University, 3400 N Charles St., 404 Krieger Hall, Baltimore, MD 21218, USA
Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 997-1000.

La formule LD=[eD+ED,b¯+B¯] (voir Goodwillie [Cyclic homology, derivations, and the free loopspace, Topology 24 (2) (1985) 187–215]) sur le complexe de Hochschild normalisé joue le rôle, en géométrie non commutative, de la formule homotopique de Cartan en homologie de Rham. Notre but est détendre cette formule au complexe de Hochschild bivariant normalisée.

The formula LD=[eD+ED,b¯+B¯] (see Goodwillie [Cyclic homology, derivations, and the free loopspace, Topology 24 (2) (1985) 187–215]) on the normalized Hochschild complex is the standard replacement in noncommutative geometry for the classical Cartan homotopy formula. Our purpose is to extend this formula to the normalized bivariant Hochschild complex.

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Accepté le :
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DOI : 10.1016/j.crma.2009.07.016
Banerjee, Abhishek 1

1 Department of Mathematics, Johns Hopkins University, 3400 N Charles St., 404 Krieger Hall, Baltimore, MD 21218, USA 
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Banerjee, Abhishek. Cartan homotopy formulae and the bivariant Hochschild complex. Comptes Rendus. Mathématique, Tome 347 (2009) no. 17-18, pp. 997-1000. doi : 10.1016/j.crma.2009.07.016. https://www.numdam.org/articles/10.1016/j.crma.2009.07.016/

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[3] Goodwillie, T.G. Cyclic homology, derivations, and the free loopspace, Topology, Volume 24 (1985) no. 2, pp. 187-215

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[7] Tsygan, B.L. Homology of matrix Lie algebras over rings and the Hochschild homology, Russian Math. Surveys, Volume 38 (1983) no. 2, pp. 198-199

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