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Rank additivity for quasi-tilted algebras of canonical type

Thomas Hübner — 1998

Colloquium Mathematicae

Given the category X of coherent sheaves over a weighted projective line X = X ( λ , p ) (of any representation type), the endomorphism ring Σ = ( 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...

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