Extremal properties for concealed-canonical algebras

Volume 130 / 2013

Michael Barot, Dirk Kussin, Helmut Lenzing Colloquium Mathematicum 130 (2013), 183-219 MSC: Primary 16G20; Secondary 14H45. DOI: 10.4064/cm130-2-4


Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of finite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commutative algebra, algebraic geometry and mathematical physics. We show that canonical algebras are characterized by a number of interesting extremal properties (among concealed-canonical algebras, that is, the endomorphism rings of tilting bundles on a weighted projective line). We also investigate the corresponding class of algebras antipodal to canonical ones. Our study yields new insights into the nature of concealed-canonical algebras, and sheds a new light on an old question: Why are the canonical algebras canonical?


  • Michael BarotInstituto de Matemáticas
    Universidad Nacional Autónoma de México
    Ciudad Universitaria
    C.P. 04510, México, D.F., México
  • Dirk KussinSettore di Matematica
    Dipartimento di Informatica
    Università degli Studi di Verona
    37134 Verona, Italy
  • Helmut LenzingInstitut für Mathematik
    Universität Paderborn
    33095 Paderborn, Germany

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