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1999 | 82 | 1 | 137-153
Tytuł artykułu

Simply connected right multipeak algebras and the separation property

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let R=k(Q,I) be a finite-dimensional algebra over a field k determined by a bound quiver (Q,I). We show that if R is a simply connected right multipeak algebra which is chord-free and $\widetilde{𝔸}$-free in the sense defined below then R has the separation property and there exists a preprojective component of the Auslander-Reiten quiver of the category prin(R) of prinjective R-modules. As a consequence we get in 4.6 a criterion for finite representation type of prin(R) in terms of the prinjective Tits quadratic form of R.
Słowa kluczowe
Rocznik
Tom
82
Numer
1
Strony
137-153
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-04-15
poprawiono
1999-07-13
Twórcy
  • Department of Mathematics and Informatics, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
  • [1] I. Assem and A. Skowroński, On some classes of simply connected algebras, Proc. London Math. Soc. 56 (1988), 417-450.
  • [2] R. Bautista, F. Larrión and L. Salmerón, On simply connected algebras, J. London Math. Soc. 27 (1983), 212-220.
  • [3] K. Bongartz, A criterion for finite representation type, Math. Ann. 269 (1984), 1-12.
  • [4] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1982), 331-378.
  • [5] O. Bretscher and P. Gabriel, The standard form of a representation-finite algebra, Bull. Soc. Math. France 111 (1983), 21-40.
  • [6] P. Dräxler, Completely separating algebras, J. Algebra 165 (1994), 550-565.
  • [7] G E. L. Green, Group-graded algebras and the zero relation problem, in: Lecture Notes in Math. 903, Springer, Berlin, 1981, 106-115.
  • [8] H.-J. von Höhne and D. Simson, Bipartite posets of finite prinjective type, J. Algebra 201 (1998), 86-114.
  • [9] K S. Kasjan, Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations, Fund. Math. 143 (1993), 259-279.
  • [10] R. Martínez-Villa and J. A. de la Pe na, The universal cover of a quiver with relations, J. Pure. Appl. Algebra 30 (1983), 277-292.
  • [11] J. A. de la Pe na and D. Simson, Prinjective modules, reflection functors, quadratic forms and Auslander-Reiten sequences, Trans. Amer. Math. Soc. 329 (1992), 733-753.
  • [12] Z. Pogorzały, On star-free bound quivers, Bull. Polish Acad. Sci. Math. 37 (1989), 255-267.
  • [13] D. Simson, Socle reductions and socle projective modules, J. Algebra 103 (1986), 18-68.
  • [14] D. Simson, A splitting theorem for multipeak path algebras, Fund. Math. 138 (1991), 112-137.
  • [15] D. Simson, Linear Representations of Partially Ordered Sets and Vector Space Categories, Algebra Logic Appl. 4, Gordon & Breach, 1992.
  • [16] D. Simson, Right peak algebras of two-separate stratified posets, their Galois coverings and socle projective modules, Comm. Algebra 20 (1992), 3541-3591.
  • [17] D. Simson, Posets of finite prinjective type and a class of orders, J. Pure Appl. Algebra 90 (1993), 77-103.
  • [18] D. Simson, Three-partite subamalgams of tiled orders of finite lattice type, ibid. 138 (1999), 151-184.
  • [19] D. Simson, Representation types, Tits reduced quadratic forms and orbit problems for lattices over orders, in: Contemp. Math. 229, Amer. Math. Soc., 1998, 307-342.
  • [20] D. Simson, Three-partite subamalgams of tiled orders of polynomial growth, Colloq. Math. 82 (1999), in press.
  • [21] A. Skowroński, Simply connected algebras and Hochschild cohomologies, in: Proc. Sixth Internat. Conf. on Representations of Algebras, CMS Conf. Proc. 14, Amer. Math. Soc., 1992, 431-447.
  • [22] H. Spanier, Algebraic Topology, McGraw-Hill, 1966.
Typ dokumentu
Bibliografia
Identyfikatory
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bwmeta1.element.bwnjournal-article-cmv82i1p137bwm
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