Abstract
Canonical algebras, introduced by C. M. Ringel in 1984, play an important role in the representation theory of nite-dimensional algebras. They also feature in many other mathematical areas like function theory, 3-manifolds, singularity theory, commuta- tive algebra, algebraic geometry and mathematical physics. We show that canonical alge- bras are characterized by a number of interesting extremal properties (among concealed- canonical algebras, that is, the endomorphism rings of tilting bundles on a weighted pro- jective 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?
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