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?
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-2-4,
author = {Michael Barot and Dirk Kussin and Helmut Lenzing},
title = {Extremal properties for concealed-canonical algebras},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {183-219},
zbl = {1288.16014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-2-4}
}
Michael Barot; Dirk Kussin; Helmut Lenzing. Extremal properties for concealed-canonical algebras. Colloquium Mathematicae, Tome 131 (2013) pp. 183-219. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm130-2-4/