Exceptional modules are tree modules

Ringel CM (1998)
In: Proceedings of the Sixth Conference of the International Linear Algebra Society. Kirkland S, Mehrmann V, Michler G, Shader B (Eds); Linear Algebra and its Applications, 276. Elsevier Science: 471-493.

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Herausgeber*in
Kirkland, Steve; Mehrmann, Volker; Michler, Gerhard; Shader, Bryan
Abstract / Bemerkung
We consider representations of a quiver over an arbitrary field. Recall that an indecomposable representation M without self-extensions is said to be exceptional. We are going to show that exceptional representations can be exhibited using matrices involving as coefficients just 0 and 1. Actually, if d is the dimension of M, there exists such a matrix presentation with precisely d-1 non-zero coefficients: the corresponding "coeffcient quiver" is a tree. (C) 1998 Elsevier Science Inc. All rights reserved.
Stichworte
partial tilting modules; preprojective and preinjective; representations; coefficient quiver; exceptional representations; 0-1-matrices; braid group; quiver; indecomposable representations
Erscheinungsjahr
1998
Titel des Konferenzbandes
Proceedings of the Sixth Conference of the International Linear Algebra Society
Band
276
Seite(n)
471-493
Konferenz
Sixth Conference of the International Linear Algebra Society
Konferenzort
Chemnitz, Germany
ISSN
0024-3795
Page URI
https://pub.uni-bielefeld.de/record/1625342

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Ringel CM. Exceptional modules are tree modules. In: Kirkland S, Mehrmann V, Michler G, Shader B, eds. Proceedings of the Sixth Conference of the International Linear Algebra Society. Linear Algebra and its Applications. Vol 276. Elsevier Science; 1998: 471-493.
Ringel, C. M. (1998). Exceptional modules are tree modules. In S. Kirkland, V. Mehrmann, G. Michler, & B. Shader (Eds.), Linear Algebra and its Applications: Vol. 276. Proceedings of the Sixth Conference of the International Linear Algebra Society (pp. 471-493). Elsevier Science. doi:10.1016/S0024-3795(97)10046-5
Ringel, C. M. (1998). “Exceptional modules are tree modules” in Proceedings of the Sixth Conference of the International Linear Algebra Society, Kirkland, S., Mehrmann, V., Michler, G., and Shader, B. eds. Linear Algebra and its Applications, vol. 276, (Elsevier Science), 471-493.
Ringel, C.M., 1998. Exceptional modules are tree modules. In S. Kirkland, et al., eds. Proceedings of the Sixth Conference of the International Linear Algebra Society. Linear Algebra and its Applications. no.276 Elsevier Science, pp. 471-493.
C.M. Ringel, “Exceptional modules are tree modules”, Proceedings of the Sixth Conference of the International Linear Algebra Society, S. Kirkland, et al., eds., Linear Algebra and its Applications, vol. 276, Elsevier Science, 1998, pp.471-493.
Ringel, C.M.: Exceptional modules are tree modules. In: Kirkland, S., Mehrmann, V., Michler, G., and Shader, B. (eds.) Proceedings of the Sixth Conference of the International Linear Algebra Society. Linear Algebra and its Applications. 276, p. 471-493. Elsevier Science (1998).
Ringel, Claus Michael. “Exceptional modules are tree modules”. Proceedings of the Sixth Conference of the International Linear Algebra Society. Ed. Steve Kirkland, Volker Mehrmann, Gerhard Michler, and Bryan Shader. Elsevier Science, 1998.Vol. 276. Linear Algebra and its Applications. 471-493.