Lectures on Representations of Quivers by William Crawley-Boevey ...
Lectures on Representations of Quivers by William Crawley-Boevey ...
Lectures on Representations of Quivers by William Crawley-Boevey ...
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(4) Auslander-Reiten theory for wild quivers. In particular, the behaviour<br />
i<br />
<strong>of</strong> the functi<strong>on</strong>s dim Hom(X, Y) for fixed X,Y.<br />
C.M.Ringel, Finite dimensi<strong>on</strong>al hereditary algebras <strong>of</strong> wild representati<strong>on</strong><br />
type, Math.Z., 161 (1978), 235-255.<br />
V.Dlab and C.M.Ringel, Eigenvalues <strong>of</strong> Coxeter transformati<strong>on</strong>s and the<br />
Gelfand-Kirillov dimensi<strong>on</strong> <strong>of</strong> the preprojective algebras, Proc. Amer.<br />
Math. Soc. 83 (1981), 228-232.<br />
D.Baer, Wild hereditary artin algebras and linear methods, Manuscripta<br />
Math. 55 (1986), 68-82.<br />
O.Kerner, Tilting wild algebras, J.L<strong>on</strong>d<strong>on</strong> Math.Soc, 39(1989), 29-47.<br />
J.A.de la Peña & M.Takane, Spectral properties <strong>of</strong> Coxeter transformati<strong>on</strong>s<br />
and applicati<strong>on</strong>s, Arch. Math. 55 (1990), 120-134.<br />
O.Kerner & F.Lukas, Regular modules over wild hereditary algebras,<br />
preprint.<br />
(5) Tame algebras <strong>of</strong> global dimensi<strong>on</strong> 2, but with properties analogous to<br />
those <strong>of</strong> path algebras: the tame c<strong>on</strong>cealed and tubular algebras.<br />
C.M.Ringel, Tame algebras and integral quadratic forms, Springer Lec. Notes<br />
1099 (1984).<br />
C.M.Ringel, Representati<strong>on</strong> theory <strong>of</strong> finite-dimensi<strong>on</strong>al algebras, in<br />
Representati<strong>on</strong>s <strong>of</strong> algebras (ed. P.Webb) L<strong>on</strong>d<strong>on</strong> Math. Soc. Lec. Note<br />
Series 116 (1986), 7-79.<br />
I.Assem & A.Skowr<strong>on</strong>ski, Algebras with cycle finite derived categories,<br />
Math. Ann., 280 (1988), 441-463.<br />
(6) Interpretati<strong>on</strong> <strong>of</strong> the representati<strong>on</strong> theory <strong>of</strong> quivers as<br />
n<strong>on</strong>-commutative algebraic geometry.<br />
H.Lenzing, Curve singularities arising from the representati<strong>on</strong> theory <strong>of</strong><br />
tame hereditary artin algebras, in Springer Lec.Notes 1177 (1986),<br />
199-231.<br />
W.Geigle & H.Lenzing, A class <strong>of</strong> weighted projective curves arising in<br />
representati<strong>on</strong> theory <strong>of</strong> finite dimensi<strong>on</strong>al algebras, in Springer Lec.<br />
Notes 1273 (1987), 265-297.<br />
(7) Tame hereditary algebras when the field is not algebraically closed,<br />
and the more ring-theoretic aspects <strong>of</strong> hereditary algebras.<br />
V.Dlab & C.M.Ringel, Indecomposable representati<strong>on</strong>s <strong>of</strong> graphs and algebras,<br />
Mem. Amer. Math. Soc., 173 (1976).<br />
C.M.Ringel, Representati<strong>on</strong>s <strong>of</strong> K-species and bimodules, J. Algebra, 41<br />
(1976), 269-302.<br />
V.Dlab & C.M.Ringel, Real subspaces <strong>of</strong> a vector space over the quaterni<strong>on</strong>s,<br />
Can. J. Math. 30 (1978), 1228-1242.<br />
A.Sch<strong>of</strong>ield, Universal localizati<strong>on</strong> for hereditary rings and quivers, in<br />
Springer Lec. Notes 1197 (1986).<br />
D.Baer, W.Geigle & H.Lenzing, The preprojective algebra <strong>of</strong> a tame<br />
hereditary Artin algebra, Comm. Algebra 15 (1987), 425-457.<br />
W.<strong>Crawley</strong>-<strong>Boevey</strong>, Regular modules for tame hereditary algebras, Proc.<br />
L<strong>on</strong>d<strong>on</strong> Math. Soc., 62 (1991), 490-508.<br />
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