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(*)-Serial coalgebras |
Hailou YAO( ), Weili FAN, Yanru PING |
| College of Applied Sciences, Beijing University of Technology, Beijing 100124, China |
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Abstract In this paper, we introduce the notion of (*)-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of (*)-serial coalgebras and their comodules, and obtain sufficient and necessary conditions for a basic coalgebra to be (*)-serial.
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| Keywords
Coalgebra
biserial comodule
(*)-serial coalgebra
quiver
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Corresponding Author(s):
YAO Hailou,Email:yaohl@bjut.edu.cn
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Issue Date: 01 October 2012
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| 1 |
Assem I, Simson D, Skowroński A. Elements of the Representation Theory of Associative Algebras, Vol 1. Cambridge: Cambridge University Press, 2006
doi: 10.1017/CBO9780511614309
|
| 2 |
Auslander M, Reiten I, Smal? S O. Representation Theory of Associative Algebras. Cambridge Studies in Advanced Mathematics, 36 . Cambridge: Cambridge University Press, 1995
|
| 3 |
Chen S W, Huang H, Zhang P. Dual Gabriel theorem with applications. Sci China, Ser A , 2006, 49: 9-26
doi: 10.1007/s11425-004-5235-4
|
| 4 |
Chin W. Special biserial coalgebras and representations of quantum SL(2). arXiv: math/0609370V2 [math, QA], 23 Mar 2011
|
| 5 |
Chin W, Montgomery S. Basic coalgebra.. In: Modular Interfaces (Riverside, CA, 1995) AMS/IP Stud Adv Math, Vol 4 . Providence: Amer Math Soc, 1997, 41-47
|
| 6 |
Cuadra J, Gómez-Torrecillas J. Idempotents and Morita-Takeuchi Theory. Comm Algebra , 2002, 30: 2405-2426
doi: 10.1081/AGB-120003476
|
| 7 |
Cuadra J, Gómez-Torrecillas J. Serial coalgebras. J Pure Appl Algebra , 2004, 189: 89-107
doi: 10.1016/j.jpaa.2003.11.005
|
| 8 |
Doi Y. Homological coalgebra. J Math Soc Japan , 1981, 33(1): 31-50
doi: 10.2969/jmsj/03310031
|
| 9 |
Drozd Y A, Kirichenko V V. Finite Dimensional Algebras. Berlin: Springer, 1994
doi: 10.1007/978-3-642-76244-4
|
| 10 |
Gómez-Torrecillas J, Nis?st?sescu C. Quasi-Frobenius coalgebras. J Algebra , 1995, 174: 909-923
doi: 10.1006/jabr.1995.1158
|
| 11 |
Gómez-Torrecillas J, Navarro G. Serial coalgebras and valued Gabriel quivers. J Algebra , 2008, 319: 5039-5059
doi: 10.1016/j.jalgebra.2008.03.020
|
| 12 |
Green J A. Locally finite representations. J Algebra , 1976, 41: 137-171
doi: 10.1016/0021-8693(76)90173-3
|
| 13 |
Kosakowska J, Simson D. Hereditary coalgebras and representations of species. J Algebra , 2005, 293: 457-505
doi: 10.1016/j.jalgebra.2005.04.019
|
| 14 |
Lin B I-Peng. Semiperfect coalgebras. J Algebra , 1977, 49: 357-373
doi: 10.1016/0021-8693(77)90246-0
|
| 15 |
Montgomery S. Hopf Algebras and Their Actions on Rings. CBMS, 82 . Providence: Amer Math Soc, 1993
|
| 16 |
Montgomery S. Indecomposable coalgebras, simple comodules and pointed Hopf algebras. Proc Amer Math Soc , 1995, 123: 2343-2351
doi: 10.1090/S0002-9939-1995-1257119-3
|
| 17 |
N?st?sescu C, Torrecillas B, Zhang Y H. Hereditary coalgebras. Comm Algebra , 1996, 24(4): 1521-1528
doi: 10.1080/00927879608825649
|
| 18 |
Nowak S, Simson D. Locally Dynkin quivers and hereditary coalgebras whose left C-comodules are direct sum of finite dimensional comodules. Comm Algebra , 2002, 30(1): 455-476
doi: 10.1081/AGB-120006503
|
| 19 |
Simson D. Coalgebras, comodules, pseudocompact algebras and tame comodule type. Colloq Math , 2001, 90: 101-150
doi: 10.4064/cm90-1-9
|
| 20 |
Simson D. Coalgebras of tame comodule type. In: Happel D, Zhang Y B, eds. Representations of Algebras, Proceedings ICRA-9, II. Beijing: Beijing Normal Univ Press, 2002, 450-486
|
| 21 |
Simson D. Path coalgebras of quivers with relations and a tame-wild dichotomy problem for coalgebras. Lecture Notes in Pure and Applied Mathematics , 2005, 236: 465-492
|
| 22 |
Simson D. Irreducible morphisms, the Gabriel-valued quiver and colocalizations for coalgebras. Int J Math Sci , 2006, 72: 1-6
doi: 10.1155/IJMMS/2006/47146
|
| 23 |
Simson D. Localizing embeddings of comodule categories with applications to tame and Euler coalgebras. J Algebra , 2007, 312: 455-494
doi: 10.1016/j.jalgebra.2006.11.043
|
| 24 |
Simson D. Coalgebras of tame comodule type, comodule categories and tame-wild dichotomy problem. In: Skowroński A, Yamata K, eds. Proc ICRA-XIV, Tokyo Aug 2010. Series of Congress Reports . Zürich: European Math Soc Publishing House, 2011
|
| 25 |
Sweedler M E. Hopf Algebras. New York: Benjamin, 1969
|
| 26 |
Woodcock D. Some categorical remarks on the representation theory of coalgebras. Comm Algebra , 1997, 25: 2775-2794
doi: 10.1080/00927879708826022
|
| 27 |
Yao Hailou, Fan Weili. Finite dimensional (*)-Serial algebras. Sci China, Ser A , 2010, 53(12): 3049 -3056
doi: 10.1007/s11425-010-4066-8
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