# Rank additivity for quasi-tilted algebras of canonical type

Colloquium Mathematicae (1998)

- Volume: 75, Issue: 2, page 183-193
- ISSN: 0010-1354

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topHübner, Thomas. "Rank additivity for quasi-tilted algebras of canonical type." Colloquium Mathematicae 75.2 (1998): 183-193. <http://eudml.org/doc/210537>.

@article{Hübner1998,

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

author = {Hübner, Thomas},

journal = {Colloquium Mathematicae},

keywords = {finite-dimensional algebras; derived categories; finite-dimensional modules; categories of coherent sheaves; weighted projective lines; almost concealed-canonical algebras; tilting sheaves; Tits quivers; indecomposable direct summands; Euler forms; rank functions; representation-infinite quasitilted algebras; rank additivity; tilting complexes},

language = {eng},

number = {2},

pages = {183-193},

title = {Rank additivity for quasi-tilted algebras of canonical type},

url = {http://eudml.org/doc/210537},

volume = {75},

year = {1998},

}

TY - JOUR

AU - Hübner, Thomas

TI - Rank additivity for quasi-tilted algebras of canonical type

JO - Colloquium Mathematicae

PY - 1998

VL - 75

IS - 2

SP - 183

EP - 193

AB - Given the category ${X}$ of coherent sheaves over a weighted projective line ${X}={X}({\lambda },{p})$ (of any representation type), the endomorphism ring $\Sigma = (\mathcal {T})$ 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 ${X}$ (Example 4.3).

LA - eng

KW - finite-dimensional algebras; derived categories; finite-dimensional modules; categories of coherent sheaves; weighted projective lines; almost concealed-canonical algebras; tilting sheaves; Tits quivers; indecomposable direct summands; Euler forms; rank functions; representation-infinite quasitilted algebras; rank additivity; tilting complexes

UR - http://eudml.org/doc/210537

ER -

## References

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- [8] H. Lenzing and H. Meltzer, Tilting sheaves and concealed-canonical algebras, in: Representation Theory of Algebras, ICRA VII, Cocoyoc 1994, CMS Conf. Proc. 18, 1996, 455-473. Zbl0863.16013
- [9] H. Lenzing and J. A. de la Pe na, Wild canonical algebras, Math. Z., to appear.
- [10] H. Lenzing and A. Skowroński, Quasi-tilted agebras of canonical type, Colloq. Math. 71 (1996), 161-181. Zbl0870.16007
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