Embedding of the vertices of the Auslander–Reiten quiver of an iterated tilted algebra of Dynkin type Δ in ZΔ
✍ Scribed by Octavio Mendoza Hernández; Marı́a Inés Platzeck
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 337 KB
- Volume
- 265
- Category
- Article
- ISSN
- 0021-8693
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✦ Synopsis
Let ∆ be a Dynkin diagram and k an algebraically closed field. Let A be an iterated tilted finitedimensional k-algebra of type ∆ and denote by  its repetitive algebra. We approach the problem of finding a combinatorial algorithm giving the embedding of the vertices of the Auslander-Reiten quiver Γ A of A in the Auslander-Reiten quiver Γ (mod( Â)) Z∆ of the stable category mod( Â). Let T be a trivial extension of finite representation type and Cartan class ∆. Assume that we know the vertices of Z∆ corresponding to the radicals of the indecomposable projective T -modules. We determine the embedding of Γ A in Z∆ for any algebra A such that T (A) T .