A Counterexample to a Conjecture of Barr

Sarah Whitehouse

We discuss two versions of a conjecture attributed to M. Barr. The Harrison cohomology of a commutative algebra is known to coincide with the Andre/Quillen cohomology over a field of characteristic zero but not in prime characteristics. The conjecture is that a modified version of Harrison cohomology, taking into account torsion, always agrees with Andre/Quillen cohomology. We give a counterexample.

Keywords: Hochschild homology, Harrison homology, Andr'e/Quillen homology.

AMS Classification (1991): 13D03, 18C15.

Theory and Applications of Categories, Vol. 2, 1996, No. 3, pp 36-39.


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