On the combinatorics of gentle algebras
Canadian Journal of Mathematics, cilt.72, sa.6, ss.1551-1580, 2020 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 72 Sayı: 6
- Basım Tarihi: 2020
- Doi Numarası: 10.4153/s0008414x19000397
- Dergi Adı: Canadian Journal of Mathematics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Sayfa Sayıları: ss.1551-1580
- Anahtar Kelimeler: Gentle algebras, τ-tilting theory
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Galatasaray Üniversitesi Adresli: Evet
Özet
For A a gentle algebra, and X and Y string modules, we construct a combinatorial basis for Hom(X, τY). We use this to describe support τ-tilting modules for A. We give a combinatorial realization of maps in both directions realizing the bijection between support τ-tilting modules and functorially finite torsion classes. We give an explicit basis of Ext1(Y, X) as short exact sequences. We analyze several constructions given in a more restricted, combinatorial setting by McConville, showing that many but not all of them can be extended to general gentle algebras.