Realizability of Modules over Tate Cohomology
نویسنده
چکیده
Let k be a field and let G be a finite group. There is a canonical element in the Hochschild cohomology of the Tate cohomology γG ∈ HH3,−1Ĥ∗(G, k) with the following property. Given a graded Ĥ∗(G, k)-module X, the image of γG in Ext 3,−1 Ĥ∗(G,k) (X,X) vanishes if and only if X is isomorphic to a direct summand of Ĥ∗(G,M) for some kG-module M . The description of the realizability obstruction works in any triangulated category with direct sums. We show that in the case of the derived category of a differential graded algebra A, there is also a canonical element of Hochschild cohomology HH3,−1H∗(A) which is a predecessor for these obstructions.
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