 Hochschild cochain complex

ID: hochschild-cochain-complex

The Hochschild cochains are

C^{n} (R, M) = Hom_{k} (R^{\otimes_{k} n}, M)

, with coboundary

(δ f) (r_{1}, \dots, r_{n + 1}) = r_{1} f (r_{2}, \dots, r_{n + 1}) + i = 1 \sum n (- 1)^{i} f (r_{1}, \dots, r_{i} r_{i + 1}, \dots, r_{n + 1}) + (- 1)^{n + 1} f (r_{1}, \dots, r_{n}) r_{n + 1} .

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