Year: 2026
Type: preprint
Abstract: We consider a family $(Λ_λ)_{λ\in \Bbbk^\times}$ of weakly symmetric algebras of Euclidean type over an algebraically closed field $\Bbbk$, where $\Bbbk^\times:= \Bbbk\setminus \{0\}$, and for each $λ\in \Bbbk^\times$, $Λ_λ$ is socle equivalent to $Λ_1$, which is the trivial extension of a hereditary algebra of type $\tilde{A}$. We compute their Hochschild cohomologies, which shows that $Λ_λ$ is not derived equivalent to $Λ_1$ if $λ\neq 1$. This means that a derived equivalence classification of weakly symmetric algebras of Euclidean type given by Bocian--Holm--Skowro{\' n}ski is not complete.
Source: arXiv (Cornell University)
Authors: Asashiba, Hideto, Itaba, Ayako, Saorin, Manuel
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1106070903, Study of Koszul AS-regular algebras in Non-commutative algebraic geometry and Hochschild cohomology theory, Diversified research of ring theory and representation theory with derived categories as its center, Bicategorical covering theory and derived equivalence classifications, G6700524545, 2-categorical covering theory for algebras, 線形圏の双圏論的被覆理論と持続加群の区間加群による近似理論
OpenAlex ID: W7221824535