Abstract
We show that the homology of the Jones annular algebras is isomorphic to that of the cyclic groups below a line of gradient 12. 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.
| Original language | English |
|---|---|
| Article number | 103 |
| Journal | Selecta Mathematica, New Series |
| Volume | 30 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - Nov 2024 |
Bibliographical note
Publisher Copyright:© The Author(s) 2024.
Funding
Special thanks are due to an anonymous referee for many helpful comments, which have greatly improved the clarity of the exposition, simplified several proofs (especially that of Proposition 2.6), and improved the ranges in the main theorems by 2. I would also like to thank Richard Hepworth for his early encouragement. The author's postdoc is funded by Gijs Heuts' ERC Starting Grant "Chromatic homotopy theory of spaces", Grant No. 950048.
| Funders | Funder number |
|---|---|
| Gijs Heuts' ERC Starting Grant "Chromatichomotopy theory of spaces" | 950048 |
Keywords
- 20J06
- Homological stability
- Jones annular algebras
- Partition algebras
- Primary 16E40
- Secondary 20B30