Twisted tensor products: Alexander-Whitney and Eilenberg-Zilber maps
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909379178004480 |
|---|---|
| author | Shepler, Anne V. Witherspoon, Sarah |
| author_facet | Shepler, Anne V. Witherspoon, Sarah |
| contents | Alexander-Whitney and Eilenberg-Zilber maps traditionally convert between the tensor product of standard resolutions and the standard resolution of a tensor product of algebras. We examine Alexander-Whitney and Eilenberg-Zilber maps for twisted tensor products, which include skew group algebras, smash products of Hopf algebras, Ore extensions, and universal enveloping algebras. These maps convert between the twist of standard resolutions and the standard resolution of a twist. We extend these to chain maps to and from twists of other resolutions. This allows one to transfer homological information between various resolutions of algebras and to expedite results on the deformation theory of twisted tensor product algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Twisted tensor products: Alexander-Whitney and Eilenberg-Zilber maps Shepler, Anne V. Witherspoon, Sarah Rings and Algebras 16E40, 16E05, 16S40, 16T05, 16S37 Alexander-Whitney and Eilenberg-Zilber maps traditionally convert between the tensor product of standard resolutions and the standard resolution of a tensor product of algebras. We examine Alexander-Whitney and Eilenberg-Zilber maps for twisted tensor products, which include skew group algebras, smash products of Hopf algebras, Ore extensions, and universal enveloping algebras. These maps convert between the twist of standard resolutions and the standard resolution of a twist. We extend these to chain maps to and from twists of other resolutions. This allows one to transfer homological information between various resolutions of algebras and to expedite results on the deformation theory of twisted tensor product algebras. |
| title | Twisted tensor products: Alexander-Whitney and Eilenberg-Zilber maps |
| topic | Rings and Algebras 16E40, 16E05, 16S40, 16T05, 16S37 |
| url | https://arxiv.org/abs/2411.04102 |