An example in the cohomology of augmented algebras (Q1115512)

This note shows that the cohomology of augmented algebras is quite sensitive to changes in the augmentation. The author gives two algebras, isomorphic as algebras but not as augmented algebras, such that the first one has a commutative cohomology and the other one not. The main tool comes from \textit{S. B. Priddy}'s work on the cohomology of Koszul algebras [Trans. Am. Math. Soc. 152, 39-60 (1970; Zbl 0261.18016)].