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Degenerations for Selfinjective Algebras of Treeclass D n
Author(s) -
Aehle Robert
Publication year - 2002
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003320
Subject(s) - quiver , isomorphism (crystallography) , mathematics , pure mathematics , algebra over a field , representation (politics) , combinatorics , crystallography , chemistry , crystal structure , politics , political science , law
Let Λ be a connected representation finite selfinjective algebra. According to G. Zwara the partial orders ⩽ ext and ⩽ deg on the isomorphism classes of d ‐dimensional Λ‐modules are equivalent if and only if the stable Auslander–Reiten quiver Γ Λ of Λ is not isomorphic to ZD 3 m /τ 2 m −1 for all m ⩾ 2. The paper describes all minimal degenerations M ⩽ deg N with M ≰ ext N in the case when Γ Λ ≅ ZD 3 m /τ 2 m −1 for some m ⩾ 2.