Coxeter functors without diagrams

Auslander, Maurice; Platzeck, María Inés; Reiten, Idun

doi:10.1090/S0002-9947-1979-0530043-2

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Coxeter functors without diagrams

Authors: Maurice Auslander, María Inés Platzeck and Idun Reiten
Journal: Trans. Amer. Math. Soc. 250 (1979), 1-46
MSC: Primary 16A64; Secondary 16A35
MathSciNet review: 530043
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Abstract: The first part of this paper is devoted to a generalization of the notion of partial Coexeter functor from diagrams to certain types of artin rings and artin algebras. The rest of the paper is devoted to a discussion of the connection between the various Coxeter functors which exist for diagrams as well as for artin rings and artin algebras.

[1] Frank W. Anderson and Kent R. Fuller, Rings and categories of modules, Springer-Verlag, New York, 1974. Graduate Texts in Mathematics, Vol. 13. MR 0417223 (54 #5281)
[2] Maurice Auslander, Representation theory of Artin algebras. I, II, Comm. Algebra 1 (1974), 177–268; ibid. 1 (1974), 269–310. MR 0349747 (50 #2240)
[3] María Inés Platzeck and Maurice Auslander, Representation theory of hereditary Artin algebras, Representation theory of algebras (Proc. Conf., Temple Univ., Philadelphia, Pa., 1976), Dekker, New York, 1978, pp. 389–424. Lecture Notes in Pure Appl. Math., Vol. 37. MR 0485999 (58 #5791)
[4] M. Auslander and I. Reiten, Notes on representation theory of artin algebras, Brandeis Univ., 1972.
[5] Maurice Auslander and Idun Reiten, Stable equivalence of Artin algebras, (Ohio State Univ., Columbus, Ohio, 1972) Springer, Berlin, 1973, pp. 8–71. Lecture Notes in Math., Vol. 353. MR 0335575 (49 #356)
[6] Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. III. Almost split sequences, Comm. Algebra 3 (1975), 239–294. MR 0379599 (52 #504)
[7] Maurice Auslander and Idun Reiten, Representation theory of Artin algebras. IV. Invariants given by almost split sequences, Comm. Algebra 5 (1977), no. 5, 443–518. MR 0439881 (55 #12762)
[8] Raymundo Bautista Ramos, Errata: “Some results on algebras of finite groups”, An. Inst. Mat. Univ. Nac. Autónoma México 8 (1968), 79 (Spanish). MR 0244397 (39 #5712)
[9] I. N. Bernšteĭn, I. M. Gel′fand, and V. A. Ponomarev, Coxeter functors, and Gabriel’s theorem, Uspehi Mat. Nauk 28 (1973), no. 2(170), 19–33 (Russian). MR 0393065 (52 #13876)
[10] Sheila Brenner and M. C. R. Butler, The equivalence of certain functors occurring in the representation theory of Artin algebras and species, J. London Math. Soc. (2) 14 (1976), no. 1, 183–187. MR 0442031 (56 #420)
[11] Henri Cartan and Samuel Eilenberg, Homological algebra, Princeton University Press, Princeton, N. J., 1956. MR 0077480 (17,1040e)
[12] Vlastimil Dlab and Claus Michael Ringel, Representations of graphs and algebras, Department of Mathematics, Carleton University, Ottawa, Ont., 1974. Carleton Mathematical Lecture Notes, No. 8. MR 0387350 (52 #8193)
[13] -, Representations of graphs and algebras, Mem. Amer. Math. Soc., No. 173 (1976).
[14] -, Representation theory of algebras, Lecture Notes in Pure and Appl. Math., vol. 37, Dekker, New York, 1978.
[15] Carl Faith, Algebra: rings, modules and categories. I, Springer-Verlag, New York, 1973. Die Grundlehren der mathematischen Wissenschaften, Band 190. MR 0366960 (51 #3206)
[16] Robert M. Fossum, Phillip A. Griffith, and Idun Reiten, Trivial extensions of abelian categories, Lecture Notes in Mathematics, Vol. 456, Springer-Verlag, Berlin, 1975. Homological algebra of trivial extensions of abelian categories with applications to ring theory. MR 0389981 (52 #10810)
[17] P. Gabriel, Répréséntations indécomposables, Séminaire Bourbaki, 26e année, (1973/74), no. 444.
[18] Edward L. Green, The representation theory of tensor algebras, J. Algebra 34 (1975), 136–171. MR 0401842 (53 #5669)
[19] Manabu Harada, Hereditary semi-primary rings and tri-angular matrix rings, Nagoya Math. J. 27 (1966), 463–484. MR 0204458 (34 #4300)
[20] Claus Michael Ringel, Representations of 𝐾-species and bimodules, J. Algebra 41 (1976), no. 2, 269–302. MR 0422350 (54 #10340)

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