 Hochschild chain complex

ID: hochschild-chain-complex

For a

k

R

and an

R

R

M

, the Hochschild chains are

C_{n} (R, M) = M \otimes_{k} R^{\otimes_{k} n} .

Their boundary is

b (m \otimes r_{1} \otimes \dots \otimes r_{n}) = m r_{1} \otimes r_{2} \otimes \dots \otimes r_{n} + i = 1 \sum n - 1 (- 1)^{i} m \otimes r_{1} \otimes \dots \otimes r_{i} r_{i + 1} \otimes \dots \otimes r_{n} + (- 1)^{n} r_{n} m \otimes r_{1} \otimes \dots \otimes r_{n - 1} .

b^{2} = 0

 New to topics? Read the docs here!