Abstract
In this paper we describe explicitly generic extensions of representations of a quiverQ of typeA. As an application, this gives rise to a description of generic extensions of representations of the\(\mathbb{F}\) q-species of typeB associated toQ together with an automorphism.
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References
Bongartz, K., On degenerations and extensions of finite dimensional modules, Adv. Math., 1996, 121: 245–287.
Reineke, M., Generic extensions and multiplicative bases of quantum groups at q = 0, Represent. Theory., 2001, 5: 147–163.
Reineke, M., Feigin’s map and monomial bases for quantized enveloping algebras, Math. Z., 2001, 237: 639–667.
Gabriel P, Unzerlegbare Darstellungen I, Manuscripta Math., 1972, 6:71–103.
Dlab, V., Ringel, C. M., Indecomposable representations of graphs and algebra, Memoirs Amer. Math. Soc., 1976, 173(6).
Auslander, M., Reiten, I., Smalφ, S. O., Representation theory of artin algebras, Cambridge Studies in Advanced Mathematics 36, Cambridge: Cambridge University Press, 1995, 123–143.
Tanisaki, T., Foldings of root systems and Gabriel’s theorem, Tsukuba J. Math., 1980, 4: 89–97.
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Chen, J. On generic extensions of representations of a Dynkin quiver of typeA . Sci. China Ser. A-Math. 48, 1083–1096 (2005). https://doi.org/10.1360/04ys0161
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DOI: https://doi.org/10.1360/04ys0161