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2014 | 12 | 1 | 39-45

Tytuł artykułu

On the number of terms in the middle of almost split sequences over cycle-finite artin algebras

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Języki publikacji

EN

Abstrakty

EN
We prove that the number of terms in the middle of an almost split sequence in the module category of a cycle-finite artin algebra is bounded by 5.

Twórcy

  • Nicolaus Copernicus University
autor
  • Centro de Investigación en Mathemáticas (CIMAT)
  • Nicolaus Copernicus University

Bibliografia

  • [1] Assem I., Simson D., Skowroński A., Elements of the Representation Theory of Associative Algebras, 1, London Math. Soc. Stud. Texts, 65, Cambridge University Press, Cambridge, 2006 http://dx.doi.org/10.1017/CBO9780511614309
  • [2] Assem I., Skowroński A., Algebras with cycle-finite derived categories, Math. Ann., 1988, 280(3), 441–463 http://dx.doi.org/10.1007/BF01456336
  • [3] Assem I., Skowroński A., Minimal representation-infinite coil algebras, Manuscripta Math., 1990, 67(3), 305–331 http://dx.doi.org/10.1007/BF02568435
  • [4] Auslander M., Representation theory of artin algebras II, Comm. Algebra, 1974, 1(4), 269–310 http://dx.doi.org/10.1080/00927877409412807
  • [5] Auslander M., Reiten I., Representation theory of artin algebras III. Almost split sequences, Comm. Algebra, 1975, 3(3), 239–294 http://dx.doi.org/10.1080/00927877508822046
  • [6] Auslander M., Reiten I., Uniserial functors, In: Representation Theory, 2, Ottawa, August 13–25, 1979, Lecture Notes in Math., 832, Springer, Berlin, 1980, 1–47
  • [7] Auslander M., Reiten I., Smalø S.O., Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math., 36, Cambridge University Press, Cambridge, 1995 http://dx.doi.org/10.1017/CBO9780511623608
  • [8] Bautista R., Brenner S., On the number of terms in the middle of an almost split sequence, In: Representations of Algebras, Puebla, August 4–8, 1980, Lecture Notes in Math., 903, Springer, Berlin, 1981, 1–8
  • [9] Brenner S., Butler M.C.R., Generalizations of the Bernstein-Gel’fand-Ponomarev reflection functors, In: Representation Theory, II, Ottawa, August 13–25, 1979, Lecture Notes in Math., 832, Springer, Berlin, 1980, 103–169
  • [10] Brenner S., Butler M.C.R., Wild subquivers of the Auslander-Reiten quiver of a tame algebra, In: Trends in the Representation Theory of Finite-Dimensional Algebras, Seattle, July 20–24, 1997, Contemp. Math., 229, American Mathematical Society, Providence, 1998, 29–48 http://dx.doi.org/10.1090/conm/229/03309
  • [11] Butler M.C.R., Ringel C.M., Auslander-Reiten sequences with few middle terms and applications to string algebras, Comm. Algebra, 1987, 15(1–2), 145–179 http://dx.doi.org/10.1080/00927878708823416
  • [12] Coelho F.U., Marcos E.N., Merklen H.A., Skowroński A., Module categories with infinite radical square zero are of finite type, Comm. Algebra, 1994, 22(11), 4511–4517 http://dx.doi.org/10.1080/00927879408825084
  • [13] Crawley-Boevey W., Tame algebras and generic modules, Proc. London Math. Soc., 1991, 63(2), 241–265 http://dx.doi.org/10.1112/plms/s3-63.2.241
  • [14] Crawley-Boevey W., Modules of finite length over their endomorphism rings, In: Representations of Algebras and Related Topics, Tsukuba, 1990, London Math. Soc. Lecture Note Series, 168, Cambridge University Press, Cambridge, 1992, 127–184 http://dx.doi.org/10.1017/CBO9780511661853.005
  • [15] Dlab V., Ringel C.M., Indecomposable Representations of Graphs and Algebras, Mem. Amer. Math. Soc., 173, American Mathematical Society, Providence, 1976
  • [16] Dlab V., Ringel C.M., The representations of tame hereditary algebras, In: Representation Theory of Algebras, Philadelphia, May 24–28, 1976, Lecture Notes in Pure Appl. Math., 37, Marcel Dekker, New York, 1978, 329–353
  • [17] Dowbor P., Skowroński A., Galois coverings of representation-infinite algebras, Comment. Math. Helv., 1987, 62(2), 311–337 http://dx.doi.org/10.1007/BF02564450
  • [18] Happel D., Ringel C.M., Tilted algebras, Trans. Amer. Math. Soc., 1982, 274(2), 399–443 http://dx.doi.org/10.1090/S0002-9947-1982-0675063-2
  • [19] Jaworska A., Malicki P., Skowroński A., Tilted algebras and short chains of modules, Math. Z., 2013, 273(1–2), 19–27 http://dx.doi.org/10.1007/s00209-012-0993-0
  • [20] Kerner O., Tilting wild algebras, J. London Math. Soc., 1989, 39(1), 29–47 http://dx.doi.org/10.1112/jlms/s2-39.1.29
  • [21] Kerner O., Stable components of wild tilted algebras, J. Algebra, 1992, 142(1), 37–57 http://dx.doi.org/10.1016/0021-8693(91)90215-T
  • [22] Kerner O., Skowroński A., On module categories with nilpotent infinite radical, Compositio Math., 1991, 77(3), 313–333
  • [23] Lenzing H., Skowroński A., Quasi-tilted algebras of canonical type, Colloq. Math., 1996, 71(2), 161–181
  • [24] Liu S.-P., Almost split sequences for nonregular modules, Fund. Math., 1993, 143(2), 183–190
  • [25] Liu S.-P., Semi-stable components of an Auslander-Reiten quiver, J. London Math. Soc., 1993, 47(3), 405–416 http://dx.doi.org/10.1112/jlms/s2-47.3.405
  • [26] Liu S.-P., Tilted algebras and generalized standard Auslander-Reiten components, Arch. Math. (Basel), 1993, 61(1), 12–19 http://dx.doi.org/10.1007/BF01258050
  • [27] Malicki P., Skowroński A., Algebras with separating almost cyclic coherent Auslander-Reiten components, J. Algebra, 2005, 291(1), 208–237 http://dx.doi.org/10.1016/j.jalgebra.2005.03.021
  • [28] de la Peña J.A., Skowroński A., Algebras with cycle-finite Galois coverings, Trans. Amer. Math. Soc., 2011, 363(8), 4309–4336 http://dx.doi.org/10.1090/S0002-9947-2011-05256-6
  • [29] de la Peña J.A., Takane M., On the number of terms in the middle of almost split sequences over tame algebras, Trans. Amer. Math. Soc., 1999, 351(9), 3857–3868 http://dx.doi.org/10.1090/S0002-9947-99-02137-6
  • [30] de la Peña J.A., Tomé B., Iterated tubular algebras, J. Pure Appl. Algebra, 1990, 64(3), 303–314 http://dx.doi.org/10.1016/0022-4049(90)90064-O
  • [31] Peng L.G., Xiao J., On the number of DTr-orbits containing directing modules, Proc. Amer. Math. Soc., 1993, 118(3), 753–756 http://dx.doi.org/10.1090/S0002-9939-1993-1135078-X
  • [32] Pogorzały Z., Skowroński A., On algebras whose indecomposable modules are multiplicity-free, Proc. London Math. Soc., 1983, 47(3), 463–479 http://dx.doi.org/10.1112/plms/s3-47.3.463
  • [33] Reiten I., Skowroński A., Characterizations of algebras with small homological dimensions, Adv. Math., 2003, 179(1), 122–154 http://dx.doi.org/10.1016/S0001-8708(02)00029-4
  • [34] Reiten I., Skowroński A., Generalized double tilted algebras, J. Math. Soc. Japan, 2004, 56(1), 269–288 http://dx.doi.org/10.2969/jmsj/1191418706
  • [35] Reiten I., Skowroński A., Smalø S.O., Short chains and regular components, Proc. Amer. Math. Soc., 1993, 117(3), 601–612 http://dx.doi.org/10.1090/S0002-9939-1993-1124149-X
  • [36] Ringel C.M., Tame Algebras and Integral Quadratic Forms, Lecture Notes in Math., 1099, Springer, Berlin, 1984
  • [37] Skowroński A., Selfinjective algebras of polynomial growth, Math. Ann., 1989, 285(2), 177–199 http://dx.doi.org/10.1007/BF01443513
  • [38] Skowroński A., Generalized standard Auslander-Reiten components without oriented cycles, Osaka J. Math., 1993, 30(3), 515–527
  • [39] Skowroński A., Regular Auslander-Reiten components containing directing modules, Proc. Amer. Math. Soc., 1994, 120(1), 19–26
  • [40] Skowroński A., Cycles in module categories, In: Finite-Dimensional Algebras and Related Topics, Ottawa, August 10–18, 1992, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 424, Kluwer, Dordrecht, 1994, 309–345
  • [41] Skowroński A., Cycle-finite algebras, J. Pure Appl. Algebra, 1995, 103(1), 105–116 http://dx.doi.org/10.1016/0022-4049(94)00094-Y
  • [42] Skowroński A., Simply connected algebras of polynomial growth, Compositio Math., 1997, 109(1), 99–133 http://dx.doi.org/10.1023/A:1000245728528
  • [43] Skowroński A., Tame algebras with strongly simply connected Galois coverings, Colloq. Math., 1997, 72(2), 335–351
  • [44] Skowroński A., Tame quasi-tilted algebras, J. Algebra, 1998, 203(2), 470–490 http://dx.doi.org/10.1006/jabr.1997.7328
  • [45] Skowroński A., Selfinjective algebras: finite and tame type, In: Trends in Representation Theory of Algebras and Related Topics, Querétaro, August 11–14, 2004, Contemp. Math., 406, American Mathematical Society, Providence, 2006, 169–238
  • [46] Skowroński A., Waschbüsch J., Representation-finite biserial algebras, J. Reine Angew. Math., 1983, 345, 172–181
  • [47] Wald B., Waschbüsch J., Tame biserial algebras, J. Algebra, 1985, 95(2), 480–500 http://dx.doi.org/10.1016/0021-8693(85)90119-X

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_s11533-013-0328-3
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