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Representation-finite triangular algebras form an open scheme

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EN
Let V be a valuation ring in an algebraically closed field K with the residue field R. Assume that A is a V-order such that the R-algebra Ā obtained from A by reduction modulo the radical of V is triangular and representation-finite. Then the K-algebra KA ≅ A ⊗V is again triangular and representation-finite. It follows by the van den Dries’s test that triangular representation-finite algebras form an open scheme.
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Tom
1
Numer
1
Strony
97-107
Opis fizyczny
Daty
wydano
2003-03-01
online
2003-03-01
Twórcy
Bibliografia
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  • [9] Ch. W. Curtis and I. Reiner, “Methods of Representation Theory”, Vol. I, Wiley Classics Library Edition, New York, 1990.
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  • [15] Ch. Jensen and H. Lenzing, Homological dimension and representation type of algebras under base field extension, Manuscripta Math., 39, 1–13 (1982). http://dx.doi.org/10.1007/BF01312441
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  • [17] S. Kasjan, On the problem of axiomatization of tame representation type, Fundamenta Mathematicae 171 (2002), 53–67 http://dx.doi.org/10.4064/fm171-1-3
  • [18] S. Kasjan, Representation-directed algebras form an open scheme, Colloq. Math. 93 (2002), 237–250.
  • [19] H. Kraft, Geometric methods in representation theory, in: Representations of algebras, 3rd int. Conf., Puebla/Mexico 1980, Lect. Notes Math. 944, 180–258 (1982).
  • [20] R. Martinez-Villa and J.A. de la Peña, The universal cover of a quiver with relations, J. Pure. Appl. Algebra 30 (1983), 277–292. http://dx.doi.org/10.1016/0022-4049(83)90062-2
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  • [24] H. Weyl, The elementary theory of convex polyhedra. in: Contrib. Theory of Games, Ann. Math. Studies 24, (1950) 3–18.
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_BF02475667
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