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A characterization of representation-finite biserial algebras over a perfect field

Seria
Rozprawy Matematyczne tom/nr w serii: 277 wydano: 1989
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Warianty tytułu
Abstrakty
EN

CONTENTS
1. Introduction.........................................................................................5
1. The structure of distributive biserial algebras.....................................7
2. Almost multiplicity-free modules........................................................15
3. One point extension..........................................................................19
4. Representation-finite biserial algebras with the (S)-condition...........31
5. Representation-finite biserial algebras ............................................41
References...........................................................................................43
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 277
Liczba stron
44
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXXVII
Daty
wydano
1989
Twórcy
  • Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, 87-100 Torun, Poland
Bibliografia
  • [1] I. Assem, Iterated tilted algebras of type $B_n$ and $C_n$, J. Algebra 84 (1983), 361-390.
  • [2] I. Assem and D. Happel, Generalized tilted algebras of type $A_n$, Comm. Algebra 9 (1981), 2102-2125.
  • [3] M. Auslander and I. Reiten, Representation theory of artin algebras III; almost split sequences, Comm. Algebra 3 (1975), 239-327.
  • [4] M. Auslander and I. Reiten, Representation theory of artin algebras; invariants given by almost split sequences, Comm. Algebra 5 (1977), 443-518.
  • [5] M. Auslander and I. Reiten, Representation theory of artin algebras; methods for computing almost split sequences and irreducible morphisms, Comm. Algebra 5 (1977), 519-554.
  • [6] M. Auslander and I. Reiten, Representation theory of artin algebras; a functorial approach to almost split sequences, Comm. Algebra 6 (1978), 257-300.
  • [7] M. Auslander and I. Reiten, Uniserial functors, in Representation Theory II, Proceedings of the Second International Conference on Representations of Algebras, Ottawa 1979, Lecture Notes in Math. 832, Springer-Verlag, Berlin 1980, 1-47.
  • [8] R. Bautista and S. Brenner, On the number of terms in the middle of an almost split-sequence, in Proceedings of the Third International Conference on Representations of Algebras, Puebla 1980, Lecture Notes in Math. 903, M. Auslander and E. Lluis (eds.), Springer-Verlag, Berlin 1981, 1-8.
  • [9] R. Bautista and F. Larrión, Auslander-Reiten quivers for certain algebras of finite representation type, J. London Math. Soc. (2) 26 (1982), 43-52.
  • [10] R. Bautista, F. Larrión and L. Salmerón, On simply connected algebras, J. London Math. Soc. (2) 27 (1983), 212-220.
  • [11] K. Bongartz and P. Gabriel, Covering spaces in representation theory, Invent. Math. 65 (1982), 331-378.
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  • [15] K. R. Fuller, Biserial rings, in Ring Theory Proceedings, Waterloo 1978, Lecture Notes in Math. 734, Springer-Verlag, Berlin 1979, 64-87.
  • [16] P. Gabriel, Auslander-Reiten sequences and representation-finite algebras, in Proceedings of the Second International Conference on Representations of Algebras, Ottawa 1979, Lecture Notes in Math. 832, Springer-Verlag, Berlin 1980, 1-71.
  • [17] P. Gabriel, The universal cover of a representation-finite algebra, in Proceedings of the Third International Conference on Representations of Algebras, Puebla 1980, Lecture Notes in Math. 903, M. Ausländer and E. Lluis (eds.), Springer-Verlag, Berlin 1981, 68-105.
  • [18] P. Gabriel and Ch. Riedtmann, Group representations without groups, Comment. Math. Helv. 54 (1979), 240-287.
  • [19] K. Igusa and G. Todorov, A characterization of finite Auslander-Reiten quivers, J. Algebra 89 (1984), 148-177.
  • [20] J. P. Jans, On the indecomposable representation of algebras, Ann. of Math. 66 (1957), 418-429.
  • [21] H. Kupisch, Unzerlegbare Moduln endicher Gruppen mit zyklischer p-Sylowgruppe, Math. Z. 108 (1969), 77-104.
  • [22] W. S. Massey, Algebraic Topology; an Introduction, Harcourt, Brace and World Inc., New York-Chicago-Atlanta 1967.
  • [23] L. A. Nazarova and A. V. Roiter, Representations of partially ordered sets, Zap. Nauch. Sem. LOMI, 28 (1972), 4-31 (in Russian).
  • [24] L. A. Nazarova and A. V. Roiter, Categorical matrix problems and the second Brauer-Thrall conjecture, preprint Inst. Math. Acad. Nauk USSR, Kiev 1975 (in Russian).
  • [25] Z. Pogorzały, Representation-finite biserial algebras over a perfect field, Bull. Pol. Ac. Sei., Math. 33 (7-8) (1985), 349-353.
  • [26] Z. Pogorzały and A. Skowroński, On algebras whose indecomposable modules are multiplicity-free, Proc. London Math. Soc. (3) 47 (1983), 463-479.
  • [27] C. M. Ringel, Report on the Brauer-Thrall conjectures: Roiter's theorem and the theorem of Nazarova and Roiter, Representation Theory I, in Proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa 1979, Lecture Notes in Math. 831, Springer-Verlag, Berlin 1980, 104-136.
  • [28] C. M. Ringel, Tame algebras, Representation theory I, in Proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa 1979, Lecture Notes in Math. 831, Springer-Verlag, Berlin 1980, 137-287.
  • [29] A. V. Roiter, The unboundedness of the dimension of the indecomposable representations of algebras that have an infinite number of indecomposable representations, Izv. Acad. Nauk SSR, 32 (1968), 1275-1282.
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  • [31] D. Simson, Representations of partially ordered sets, vector space categories and socle projective modules, preprint, Paderborn 1983.
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  • [33] A. Skowroński and J. Waschbüsch, Representation-finite biserial algebras, J. Reine Angew. Math. 345 (1983), 172-181.
  • [34] J. Waschbüsch, Eine Klasse von Quasi-Frobenius-Algebren und ihre unzerlegbaren Moduln, J. Algebra 62 (1981), 372-401.
  • [35] J. Waschbüsch, Universal coverings of selfinjective algebras, in Proceedings of the Thrid International Conference on Representations of Algebras, Puebla 1980, Lecture Notes in Math. 903, M. Auslander and E. Lluis (eds.), Springer-Verlag, Berlin 1981, 331-349.
Języki publikacji
EN
Uwagi
1980 Mathematics Subject Classification: Primary 16A46
Identyfikator YADDA
bwmeta1.element.zamlynska-44b23f22-d011-440f-948b-a97aba76cb4a
Identyfikatory
ISBN
83-01-08944-X
ISSN
0012-3862
Kolekcja
DML-PL
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