Geodesic
Extremal properties for concealed-canonical algebras
Michael Barot 1   ; Dirk Kussin 2   ; Helmut Lenzing 3
1 Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria C.P. 04510, México, D.F., México
2 Settore di Matematica Dipartimento di Informatica Università degli Studi di Verona 37134 Verona, Italy
3 Institut für Mathematik Universität Paderborn 33095 Paderborn, Germany
Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 183-219 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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?
DOI : 10.4064/cm130-2-4
Keywords: canonical algebras introduced ringel play important role representation theory finite dimensional algebras feature many other mathematical areas function theory manifolds singularity theory commutative algebra algebraic geometry mathematical physics canonical algebras characterized number interesting extremal properties among concealed canonical algebras endomorphism rings tilting bundles weighted projective line investigate corresponding class algebras antipodal canonical study yields insights nature concealed canonical algebras sheds light old question why canonical algebras canonical

Michael Barot  1   ; Dirk Kussin  2   ; Helmut Lenzing  3

1 Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria C.P. 04510, México, D.F., México
2 Settore di Matematica Dipartimento di Informatica Università degli Studi di Verona 37134 Verona, Italy
3 Institut für Mathematik Universität Paderborn 33095 Paderborn, Germany 
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Michael Barot; Dirk Kussin; Helmut Lenzing. Extremal properties for concealed-canonical algebras. Colloquium Mathematicum, Tome 130 (2013) no. 2, pp. 183-219. doi: 10.4064/cm130-2-4

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