Replacing bar-like resolutions in a simplicial setting
Rings and Algebras
2024-04-10 v1
Abstract
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, one uses a bar-like resolution in a simplicial setting 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.
Cite
@article{arxiv.2404.06368,
title = {Replacing bar-like resolutions in a simplicial setting},
author = {Samuel Carolus and Jacob Laubacher and Sydney D. Vitalbo and Leah K. Widlarz},
journal= {arXiv preprint arXiv:2404.06368},
year = {2024}
}
Comments
9 pages, comments welcome. arXiv admin note: text overlap with arXiv:1707.03863