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Quivers and their representations

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References

  1. I.N. Berstein, I.M. Gel’fand, V.A. Ponomarev, vol.28, N.2, 1973, p.19-33 (in Russian); English translation: Russian Math. Surveys, v.28, No.2, 1973, p.17-32.

    Google Scholar 

  2. N. Bourbaki, Croups et algèbres de Lie, Chaptires 4,5,6. Paris, Hermann, 1968.

    Google Scholar 

  3. W. Crawley-Boevey, Lectures on Representations of Quivers. In: < http://www.amsta.leeds.ac.uk/ pmtwc/quivlecs.pdf >.

    Google Scholar 

  4. V. Dlab and C.M. Ringel, On algebras of finite representation type, Carleton Math. Lecture Notes, N.2, Carleton Univ., Ottawa, 1973, 160pp.

    Google Scholar 

  5. V. Dlab and C.M. Ringel, Representations of graphs and algebras, Carleton Math. Lecture Notes, N.8, Carleton Univ., Ottawa, 1974, N.8, 85p.

    Google Scholar 

  6. V. Dlab and C.M. Ringel, On algebras of finite representation type, J. Algebra, 1975, v.33, N.2, p.306-394.

    Article  MATH  MathSciNet  Google Scholar 

  7. V. Dlab, C.M. Ringel, Indecomposable representations of graphs and algebras, Memoirs Amer. Math. Soc., vol.173, 1976.

    Google Scholar 

  8. P. Donovan and M.R. Freislich, Some evidence for an extension of the Brauer-Thrall conjecture, Sonderforschungsbereich Theor. Math., v.40, 1972, p.24-26.

    Google Scholar 

  9. P. Donovan, M.R. Freislich, The representation theory of finite graphs and associated algebras, Carleton Math. Lecture Notes, No.5, Carleton Univ., Ottawa, 1973, 83p.

    Google Scholar 

  10. P. Donovan and M. Freislich, Indecomposable representations of certain commutative quivers, Bull. Austral. Math. Soc., v.20, 1979, p.17-34.

    MATH  MathSciNet  Google Scholar 

  11. S. Eilenberg, A. Rosenberg and D. Zelinsky, On the dimension of modules and algebras, VIII, Nagoya Math. J., v.12, 1957, p.71-93.

    MATH  MathSciNet  Google Scholar 

  12. P. Gabriel, Unzerlegbare Darstellungen I, Manuscripta Math., v.6, 1972, p.71-103.

    Article  MathSciNet  Google Scholar 

  13. P. Gabriel, Indecomposable represenations II, Instit. Naz. Alta Mat., Symp. Math., 1973, v.11, p.81-104.

    MathSciNet  Google Scholar 

  14. H. Grassmann, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik, Teubner, 1844.

    Google Scholar 

  15. E. Green, The representation theory of tensor algebras, J. Algebra, v.34, 1975, p.135-171.

    Google Scholar 

  16. W.H. Gustafson, The history of algebras and their representations, Lecture Notes Math., v.944, 1982, p.1-28.

    MathSciNet  Google Scholar 

  17. G. Hochschild, The structure of algebras with nonzero radical, Bull. Amer. Math. Soc., vol.53, 1947, p.369-377.

    Article  MATH  MathSciNet  Google Scholar 

  18. G. Hochschild, Note on maximal algebras, Proc. Amer. Math. Soc., v.1, 1950, p.11-14.

    Article  MATH  MathSciNet  Google Scholar 

  19. G. Hochschild, Note on relative homological dimension, Nagaya Math. J., v.13, 1958, p.89-94.

    MATH  MathSciNet  Google Scholar 

  20. Jin Hong, Seok-Jin Kang, Introduction to quantum groups and crystal bases, American Mathematical Society, 2002.

    Google Scholar 

  21. J.P. Jans and T. Nakayama, On the dimension of modules and algebras, VII, Nagoya Math. J., vol.11, 1957, p.67-76.

    MATH  MathSciNet  Google Scholar 

  22. V. Kac, Infinite root systems, representations of graphs and invariant theory, Invent. Math., v.56, 1980, p.57-92.

    Article  MATH  MathSciNet  Google Scholar 

  23. V. Kac, Some remarks on representations of quivers and infinite root systems, Carleton Math. Lecture Notes, v.25, 1980, p.1301-1317.

    Google Scholar 

  24. V. Kac, Infinite dimensional Lie algebras, Cambridge Univ. Press, 1985.

    Google Scholar 

  25. L.A. Nazarova, Representations of quivers of infinite type, Izv. Akad. Nauk SSSR, Ser.Mat., vol.37, 1973, p.752-791 (in Russian); English translation: Math. USSR Izv., vol.7, 1973, p.749-792.

    MATH  MathSciNet  Google Scholar 

  26. S.A. Ovsienko, The representations of quivers with relations, Matrix problems, Kiev, 1977, p.88-103 (in Russian).

    Google Scholar 

  27. S.A. Ovsienko, A.V. Roiter, Bilinear forms and categories of representations, Matrix problems, Kiev, 1977, p.71-80 (in Russian).

    Google Scholar 

  28. C. Ringel, The representation type of local algebras, Springer LNM, v.488, 1975, p.282-305.

    MathSciNet  Google Scholar 

  29. C.M. Ringel, Representations of K-species and bimodules, J. Algebra, v.41, 1976, p.269-302.

    Article  MATH  MathSciNet  Google Scholar 

  30. C. Ringel, Tame algebras (On algorithms for solving vector space problems II), Carleton Math. Lecture Notes, v.25, 1980, p.1-32.

    Google Scholar 

  31. C. Ringel, Four papers in linear algebra. In: I.M.Gelfand a.o (eds), Representation theory, London Math. Soc., 1982, 141-156.

    Google Scholar 

  32. Yu. V. Roganov, The dimension of a tensor algebra of a projective bimodule, Mat. Zam., v.18, No.6, 1975, p.895-902.

    Google Scholar 

  33. V. Romanovskij and A.S. Shkabara, The representation of diagrams with one relation, Mat. Sbornik, Kiev, 1976, p.282-285 (in Russian).

    Google Scholar 

  34. A. Shkabara, Quivers with relations and DGC, In: Representations of quivers with relations, Preprint 78.43, Kiev, Institute of Mathematics AN USSR, 1978, p.3-41 (in Russian).

    Google Scholar 

  35. A.S. Shkabara, Commutative quivers of tame type I, Preprint 78.42, Kiev, Institute of Mathematics AN USSR, 1978, 56p. (in Russian).

    Google Scholar 

  36. Zhe-Xian Wan, Introduction to Kac-Moody algebra, World Scientific, 1991.

    Google Scholar 

  37. T. Yoshii, Notes on algebras of bounded representation type, Proc. Japan Acad., v.32, 1956, p.441-445.

    Article  MATH  MathSciNet  Google Scholar 

  38. T. Yoshii, On algebras of bounded representation type, Osaka Math. J., v.8, 1956, p.51-105; Supplements and corrections; bib., v.9, 1957, p.67-85.

    MATH  MathSciNet  Google Scholar 

  39. T. Yoshii, On the indecomposable representations of algebras, Ann. Math., v.66, 1957, p.418-429.

    Article  Google Scholar 

  40. A.G. Zavadskij, A.S. Shkabara, Commutative quivers and matrix algebras of finite type, Preprint 76.3, Kiev, Institute of Mathematics AN USSR, 1976, 52p. (in Russian).

    Google Scholar 

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Hazewinkel, M., Gubareni, N., Kirichenko, V. (2007). Quivers and their representations. In: Hazewinkel, M., Gubareni, N., Kirichenko, V. (eds) Algebras, Rings and Modules. Mathematics and Its Applications, vol 586. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5141-8_2

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