Mathematics > K-Theory and Homology
arXiv:2509.05135 (math)
[Submitted on 5 Sep 2025 (v1), last revised 17 Jun 2026 (this version, v2)]
Abstract:We introduce the $\tau$-Hochschild (co)homology of a finite dimensional associative algebra $\Lambda$ by means of the higher Auslander-Reiten translate of O. Iyama. We show that the global dimension of $\Lambda$, Happel's question and Han's conjecture are related to the $\tau$-Hochschild (co)homology.
| Comments: | 27 pages, minor changes. To appear in Annals of K-Theory |
| Subjects: | K-Theory and Homology (math.KT); Rings and Algebras (math.RA); Representation Theory (math.RT) |
| MSC classes: | 16E40 (Primary) 16G70, 16D20, 16E30 (Secondary) |
| Cite as: | arXiv:2509.05135 [math.KT] |
| (or arXiv:2509.05135v2 [math.KT] for this version) | |
| https://doi.org/10.48550/arXiv.2509.05135 arXiv-issued DOI via DataCite |
Submission history
From: Claude Cibils [view email]
[v1]
Fri, 5 Sep 2025 14:24:23 UTC (26 KB)
[v2]
Wed, 17 Jun 2026 11:31:46 UTC (23 KB)
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