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A counterexample to a conjecture of Barr. (English) Zbl 0864.19003

Summary: We discuss two versions of a conjecture attributed to M. Barr [cf. M. Gerstenhaber and S. D. Schack, J. Pure Appl. Algebra 48, 229-247 (1987; Zbl 0671.13007), p. 232]. The Harrison cohomology of a commutative algebra is known to coincide with the André/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 André/Quillen cohomology. We give a counterexample.

MSC:

19D55 \(K\)-theory and homology; cyclic homology and cohomology
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
18C15 Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads
18G60 Other (co)homology theories (MSC2010)

Citations:

Zbl 0671.13007
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