PreprintCC BY 4.0arXiv
On a derived equivalence classification of weakly symmetric algebras of Euclidean type
Abstract
We consider a family (Λλ)λ∈ Bbbk× of weakly symmetric algebras of Euclidean type over an algebraically closed field Bbbk, where Bbbk×:= Bbbk∖ {0}, and for each λ∈ Bbbk×, Λλ is socle equivalent to Λ1, which is the trivial extension of a hereditary algebra of type Ã. We compute their Hochschild cohomologies, which shows that Λλ is not derived equivalent to Λ1 if λ≠ 1. This means that a derived equivalence classification of weakly symmetric algebras of Euclidean type given by Bocian--Holm--Skowro{\' n}ski is not complete.
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BibTeX
@misc{asashiba2026derived,
title = {{On a derived equivalence classification of weakly symmetric algebras of Euclidean type}},
author = {Hideto Asashiba and Ayako Itaba and Manuel Saorin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15517},
eprint = {2610.15517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15517},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On a derived equivalence classification of weakly symmetric algebras of Euclidean type
AU - Hideto Asashiba
AU - Ayako Itaba
AU - Manuel Saorin
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15517
UR - https://arxiv.org/abs/2610.15517
AB - We consider a family (Λ_λ)_λ∈ Bbbk^× of weakly symmetric algebras of Euclidean type over an algebraically closed field Bbbk, where Bbbk^×:= Bbbk∖ {0}, and for each λ∈ Bbbk^×, Λ_λ is socle equivalent to Λ_1, which is the trivial extension of a hereditary algebra of type Ã. We compute their Hochschild cohomologies, which shows that Λ_λ is not derived equivalent to Λ_1 if λ≠ 1. This means that a derived equivalence classification of weakly symmetric algebras of Euclidean type given by Bocian--Holm--Skowro{\' n}ski is not complete.
ER -