Zur Homologietheorie der assoziativen Algebren

Abstract

Let K be a commutative ring, R a commutative K-algebra, and S:=R⊗R the enveloping algebra of R. We define a differential graded S-algebra M. Let R be a protective K-module. Then M is an S-free resolution of R which is better suited for the computation of the (co)homology of R than Hochschild's standard complex, since M is smaller. If, e. g., K is noetherian and R is a finitely generated K-algebra, all M_i are noetherian S-modules. As an application we show that, if R contains the rationals, the canonical morphism of graded R-algebras Λ_RTor ^S₁ (R,R)→Tor^S(R,R) has a left inverse.