Rank additivity for quasi-tilted algebras of canonical type

Volume 75 / 1998

Thomas Hübner Colloquium Mathematicum 75 (1998), 183-193 DOI: 10.4064/cm-75-2-183-193

Abstract

Given the category $\coh\sym{X}$ of coherent sheaves over a weighted projective line $\sym{X}=\sym{X}(\und{\lambda},\und{p})$ (of any representation type), the endomorphism ring $\mit\Sigma = \End(\cal{T})$ 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 $\coh\sym{X}$ (Example 4.3).

Authors

  • Thomas Hübner

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