Simplicial and crossed resolutions of commutative algebras (Q1913961)

The authors relate \textit{M. André}'s construction [``Homologie des algèbres commutatives'', Grundlehren 206 (1974; Zbl 0284.18009)] of the simplicial resolution of an algebra to an obvious construction of its crossed resolution [\textit{T. Porter}, J. Algebra 109, 415-429 (1987; Zbl 0619.16033)]. This construction does give a ``step-by-step'' construction of a crossed resolution, and an explicit description of this in low dimensions is presented. Thus, ``combinatorial algebra theory'' by analogy with ``combinatorial group theory'' contains some important new ideas.