抄録
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.
