Rank additivity for quasi-tilted algebras of canonical type

Thomas Hübner
1998 Colloquium Mathematicum  
Given the category coh X of coherent sheaves over a weighted projective line X = X(λ, p) (of any representation type), the endomorphism ring Σ = End(T ) of an arbitrary tilting sheaf-which is by definition an almost concealed canonical algebra-is shown to satisfy a rank additivity property (Theorem 3.2). Moreover, this property extends to the representationinfinite quasi-tilted algebras of canonical type (Theorem 4.2). Finally, it is demonstrated that rank additivity does not generalize to the case of tilting complexes over coh X (Example 4.3).
doi:10.4064/cm-75-2-183-193 fatcat:wwlp3k4nsnfzvby4w45w3vk76a