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Soient un anneau commutatif et une -algèbre associative quelconque. Nous calculons le groupe d’homologie de la -algèbre de Lie des matrices de “trace nulle” sur . Le groupe ainsi déterminé est un groupe d’homologie d’un complexe inspiré d’A. Connes; il est isomorphe à lorsque est commutative. Nous obtenons également des résultats pour un groupe d’homologie relative associé à une surjection de -algèbres. Les démonstrations utilisent la classification des extensions centrales et des...
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