Relative cyclic homology of square zero extensions

Details Relative cyclic homology of square zero extensions Relative cyclic homology of square zero extensions

2004-08-27

arxiv.org/abs/math/0408389v4

Mathematics

K-Theory and Homology

24 pages. Definitive version, to appear in Crelle Journal

Scientific paper

Let k be a characteristic zero field, C a k-algebra and M a square zero two sided ideal of C. We obtain a new mixed complex, simpler that the canonical one, giving the Hochschild and cyclic homologies of C relative to M. This complex resembles the canonical reduced mixed complex of an augmented algebra. We begin the study of our complex showing that it has a harmonic decomposition like to the one considered by Cuntz and Quillen for the normalized mixed complex of an algebra. We also give new proofs of two theorems of Goodwillie, obtaining an improvement of one of them.

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