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Graphs with relations, coverings and group-graded algebras
Author:
Edward L. Green
Journal:
Trans. Amer. Math. Soc. 279 (1983), 297-310
MSC:
Primary 16A64; Secondary 05C20, 16A03, 16A90, 57M10
MathSciNet review:
704617
Full-text PDF Free Access
Abstract |
References |
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Additional Information
Abstract: The paper studies the interrelationship between coverings of finite directed graphs and gradings of the path algebras associated to the directed graphs. To include gradings of all basic finite-dimensional algebras over an algebraically closed field, a theory of coverings of graphs with relations is introduced.
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Peter
Gabriel, Auslander-Reiten sequences and representation-finite
algebras, Representation theory, I (Proc. Workshop, Carleton Univ.,
Ottawa, Ont., 1979), Lecture Notes in Math., vol. 831, Springer,
Berlin, 1980, pp. 1–71. MR 607140
(82i:16030)
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-, Coverings in representation theory, Talk at ICRA III, Puebla, Mexico, 1980.
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Robert
Gordon and Edward
L. Green, Graded Artin algebras, J. Algebra
76 (1982), no. 1, 111–137. MR 659212
(83m:16028a), http://dx.doi.org/10.1016/0021-8693(82)90240-X
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Robert
Gordon and Edward
L. Green, Representation theory of graded Artin algebras, J.
Algebra 76 (1982), no. 1, 138–152. MR 659213
(83m:16028b), http://dx.doi.org/10.1016/0021-8693(82)90241-1
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E. G. Green, Representation theory of tensor algebras, Thesis, Brandeis University, 1973.
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Edward
L. Green, The representation theory of tensor algebras, J.
Algebra 34 (1975), 136–171. MR 0401842
(53 #5669)
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-, Group-graded algebras and the zero relation problem, Proc. ICRA III, Puebla, Mexico, 1980 (to appear).
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William
S. Massey, Algebraic topology: An introduction, Harcourt,
Brace & World, Inc., New York, 1967. MR 0211390
(35 #2271)
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C.
Riedtmann, Algebren, Darstellungsköcher, Überlagerungen
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no. 2, 199–224 (German). MR 576602
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- [1]
- Peter Gabriel, Auslander-Reiten sequences and representation-finite algebras, Representation Theory 1 (Dlab and Gabriel, Editors), Lecture Notes in Math., vol. 831, Springer-Verlag, Berlin and New York, 1980. MR 607140 (82i:16030)
- [2]
- -, Coverings in representation theory, Talk at ICRA III, Puebla, Mexico, 1980.
- [3]
- R. Gordon and E. L. Green, Graded Art in algebras, J. Algebra 76 (1982), 111-137. MR 659212 (83m:16028a)
- [4]
- -, Representation theory of graded Artin algebras, J. Algebra 76 (1982), 138-152. MR 659213 (83m:16028b)
- [5]
- E. G. Green, Representation theory of tensor algebras, Thesis, Brandeis University, 1973.
- [6]
- -, Representation theory of tensor algebras, J. Algebra 34 1975), 136-171. MR 0401842 (53:5669)
- [7]
- -, Group-graded algebras and the zero relation problem, Proc. ICRA III, Puebla, Mexico, 1980 (to appear).
- [8]
- William S. Massey, Algebraic topology: An introduction, Harcourt, Brace & World, New York, 1967. MR 0211390 (35:2271)
- [9]
- Christine Riedtmann, Algebren, Darstellungsköcher, Uberlagerungen and Zurück, Comment. Math. Helv. 55 (1980), 199-224. MR 576602 (82k:16039)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1983-0704617-0
PII:
S 0002-9947(1983)0704617-0
Article copyright:
© Copyright 1983 American Mathematical Society
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