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Let A with d be a differential graded associative algebra (DG algebra). What is the definition of Hochschild complex C*(A,A)? There should be a Hoshschild differential and a cup product, but i can't find the reference that specifies the formula. Does any one know?

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A formula appears here arxiv.org/pdf/math/0211229v1.pdf, probably a repeat question... –  Daniel Pomerleano Aug 4 '12 at 18:36
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Or try this one: math.sciences.univnantes.fr/~hossein/Publications/…, page 4, since you also wanted a formula for cup product. Sign conventions often differ and it's important to have ones which are consistent. –  Daniel Pomerleano Aug 4 '12 at 18:46
    

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