Geodesic
A lower bound on the homological bidimension of a non-unital C*-algebra
Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 435-444

Voir la notice de l'article provenant de la source Cambridge University Press

Let A be a C*-algebra. For each Banach A-bimodule X, the second continuous Hochschild cohomology group H2(A, X) of A with coefficients in X is defined (see [6]); there is a natural correspondence between the elements of this group and equivalence classes of singular, admissible extensions of A by X. Specifically this means that H2(A, X) ≠ {0} for some X if and only if there exists a Banach algebra B with Jacobson radical R such that R2 = {0}, R is complemented as a Banach space, and B/R ≅ A, but B has no strong Wedderburn decomposition; i.e., there is no closed subalgebra C of B such that B ≅ C © R. In turn this is equivalent to db A ≥ 2, where db A is the homological bidimension of A; i.e., the homological dimension of A#, the unitization of A, as an,A-bimodule [6, III. 5.15]. This paper is concerned with the following basic question, which was posed in [7]. 
Ermert, Olaf. A lower bound on the homological bidimension of a non-unital C*-algebra. Glasgow mathematical journal, Tome 40 (1998) no. 3, pp. 435-444. doi: 10.1017/S0017089500032778
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