Replacing bar-like resolutions in a simplicial setting

It is well known that the bar resolution can be replaced with any projective resolution of the corresponding algebra when computing the Hochschild (co)homology of that algebra. This is, in fact, a feature of its construction via derived functors. For generalizations and extensions of the Hochschild (co)homology (like the secondary and tertiary Hochschild (co)homology theory, as well as higher order Hochschild (co)homology theory), one uses a bar-like resolution in a simplicial setting within its construction in order to accommodate the changing module structures in every dimension. In this note, we present a method in order to replace these bar-like resolutions.

کلیدواژه ها:

Simplicial modules ، Hochschild homology ، resolutions