Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9947-1979-0530043-2
MathSciNet review: 530043
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] F. W. Anderson and K. R. Fuller, Rings and categories of modules, Graduate Texts in Mathematics, no. 13, Springer-Verlag, Berlin and New York, 1974. MR 0417223 (54:5281)
  • [2] M. Auslander, Representation theory of artin algebras. I, Comm. Algebra 1 (1974), 177-268. MR 0349747 (50:2240)
  • [3] M. Auslander and M. I. Platzeck, Representation theory of hereditary artin algebras, Lecture Notes in Pure and Appl. Math., vol. 37 Dekker, New York, 1978. MR 0485999 (58:5791)
  • [4] M. Auslander and I. Reiten, Notes on representation theory of artin algebras, Brandeis Univ., 1972.
  • [5] -, Stable equivalence of artin algebras, Lecture Notes in Math., vol. 353, Springer-Verlag, Berlin and New York, 1973. MR 0335575 (49:356)
  • [6] -, Representation theory of artin algebras. III, Almost split sequences, Comm. Algebra 3 (1975), 239-294. MR 0379599 (52:504)
  • [7] -, Representation theory of artin algebras. IV, Comm. Algebra 5 (1977), 443-518. MR 0439881 (55:12762)
  • [8] R. Bautista, Algebras close to hereditary algebras (to appear). MR 0244397 (39:5712)
  • [9] I. N. Bernstein, I. M. Gelfand and V. A. Ponomarev, Coxeter functors and a theorem of Gabriel, Uspehi Mat. Nauk 28 (1973), 19-33 = Russian Math. Surveys 28 (1973), 17-32. MR 0393065 (52:13876)
  • [10] S. 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. 14 (1976), 183-187. MR 0442031 (56:420)
  • [11] E. Cartan and S. Eilenberg, Homological algebra, Princeton Univ. Press, Princeton, N. J., 1956. MR 0077480 (17:1040e)
  • [12] V. Dlab and C. M. Ringel, Representations of graphs and algebras, J. Algebra 33 (1975), 306-394. 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] C. Faith, Algebra: Rings, modules and categories. I, Die Grundlehren der math. Wissenschaften, Band 190, Springer-Verlag, Berlin and New York, 1973. MR 0366960 (51:3206)
  • [16] R. Fossum, P. Griffith and I. Reiten, Trivial extensions of abelian categories, Lecture Notes in Math., vol. 456, Springer-Verlag, Berlin and New York, 1975. MR 0389981 (52:10810)
  • [17] P. Gabriel, Répréséntations indécomposables, Séminaire Bourbaki, 26e année, (1973/74), no. 444.
  • [18] E. Green, The representation theory of tensor algebras, J. Algebra 34 (1975), 136-171. MR 0401842 (53:5669)
  • [19] M. Harada, Hereditary semiprimary rings and triangular matrix rings, Nagoya Math. J. 27 (1966), 463-484. MR 0204458 (34:4300)
  • [20] C. M. Ringel, Representations of K-species and bimodules, J. Algebra 41 (1976), 269-302. MR 0422350 (54:10340)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 16A64, 16A35

Retrieve articles in all journals with MSC: 16A64, 16A35


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1979-0530043-2
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society