Homology of Rook-Brauer Algebras and Motzkin Algebras
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913863406977024 |
|---|---|
| author | Ta, Khoa |
| author_facet | Ta, Khoa |
| contents | Using the technique of inductive resolution introduced in arXiv:2303.07979, we prove that the homology of Rook-Brauer Algebra, interpreted as appropriate Tor-group, is isomorphic to that of symmetric group for all degrees under the assumption that $ε$ in $R$ is invertible; furthermore, we also prove the homology of the Motzkin algebras vanishes in positive degrees under the same assumption. These results thereby establish homological stability of both algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21977 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homology of Rook-Brauer Algebras and Motzkin Algebras Ta, Khoa Rings and Algebras Representation Theory Using the technique of inductive resolution introduced in arXiv:2303.07979, we prove that the homology of Rook-Brauer Algebra, interpreted as appropriate Tor-group, is isomorphic to that of symmetric group for all degrees under the assumption that $ε$ in $R$ is invertible; furthermore, we also prove the homology of the Motzkin algebras vanishes in positive degrees under the same assumption. These results thereby establish homological stability of both algebras. |
| title | Homology of Rook-Brauer Algebras and Motzkin Algebras |
| topic | Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2505.21977 |