2006 年 64 巻 1 号 p. 103-129
We generalize the techniques developed in the previous paper [10] on free algebras and free bimodules to path algebras and projective bimodules. We develop the theory of Gröber bases on path algebras and their projective bimodules, and use it to construct projective resolutions of bimodules over a quotient algebra of a path algebra. It gives an effective way to calculate the Hochschild cohomology of algebras expressed as quotients of path algebras. We also give a formula for the cup product in the cohomology in terms of our resolution. It gives a way to determine the ring structure of the cohomology.
