Stable homology isomorphisms for the partition and Jones annular algebras
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909751819894784 |
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| author | Boyde, Guy |
| author_facet | Boyde, Guy |
| contents | We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient $\frac{1}{2}$. We also show that the homology of the partition algebras is isomorphic to that of the symmetric groups below a line of gradient 1, strengthening a result of Boyd-Hepworth-Patzt. Both isomorphisms hold in a range exceeding the stability range of the algebras in question. Along the way, we prove the usual odd-strand and invertible parameter results for the Jones annular algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03214 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stable homology isomorphisms for the partition and Jones annular algebras Boyde, Guy Algebraic Topology Geometric Topology Representation Theory 16E40, 20J06 (Primary) 20B30 (Secondary) We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient $\frac{1}{2}$. We also show that the homology of the partition algebras is isomorphic to that of the symmetric groups below a line of gradient 1, strengthening a result of Boyd-Hepworth-Patzt. Both isomorphisms hold in a range exceeding the stability range of the algebras in question. Along the way, we prove the usual odd-strand and invertible parameter results for the Jones annular algebras. |
| title | Stable homology isomorphisms for the partition and Jones annular algebras |
| topic | Algebraic Topology Geometric Topology Representation Theory 16E40, 20J06 (Primary) 20B30 (Secondary) |
| url | https://arxiv.org/abs/2308.03214 |