Extremal properties for concealed-canonical algebras

Michael Barot, Dirk Kussin, and Helmut Lenzing. "Extremal properties for concealed-canonical algebras." Colloquium Mathematicae 130.2 (2013): 183-219. <http://eudml.org/doc/283435>.

@article{MichaelBarot2013,
abstract = {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?},
author = {Michael Barot, Dirk Kussin, Helmut Lenzing},
journal = {Colloquium Mathematicae},
keywords = {canonical algebras; concealed-canonical algebras; weighted projective lines; representation types; finite-dimensional algebras; tilting bundles; line bundles; Hübner reflections; tubular mutations; tame domestic algebras},
language = {eng},
number = {2},
pages = {183-219},
title = {Extremal properties for concealed-canonical algebras},
url = {http://eudml.org/doc/283435},
volume = {130},
year = {2013},
}

TY - JOUR
AU - Michael Barot
AU - Dirk Kussin
AU - Helmut Lenzing
TI - Extremal properties for concealed-canonical algebras
JO - Colloquium Mathematicae
PY - 2013
VL - 130
IS - 2
SP - 183
EP - 219
AB - 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?
LA - eng
KW - canonical algebras; concealed-canonical algebras; weighted projective lines; representation types; finite-dimensional algebras; tilting bundles; line bundles; Hübner reflections; tubular mutations; tame domestic algebras
UR - http://eudml.org/doc/283435
ER -