On the representation type of certain trivial extensions
DOI:
https://doi.org/10.4067/S0716-09172001000300005Abstract
Let A ?= kQ/I be a basic and connected finite dimension algebra over closed field k. In this note show that in case B = A[M] is a tame one-point extension of a tame concealed algebra A by an indecomposable module M, then the trivial extension T(B) = B ? DB is tame if and only if the module M is regular.References
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[P] J.A. de la Peña. On the representation type of one point extension of tame concealed algebras. Manuscripta Math., 61; 183– 194, (1988).
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[AS2] I. Assem and A. Skowronski. On tame repetitive algebra. Fundamenta Mathematicae. 142; 59–84, (1993).
[ARS] M. Auslander, I. Reiten and S. Smalø. Representation theory of Artin algebras. Cambridge Studies in Advanced Mathematics 36, (1995).
[BL] M. Barot and H. Lenzing. One-point extensions and derived equivalence. to appear.
[BP] M. Barot and J. A. de la Peña. Derived tubular strongly simply connected algebras. In Proceeding Am. Math. Soc. 127 N 3, 647–655, (1999).
[C-B] W.W. Crawley-Boevey. Funtorial filtration II: Clans and the Gelfand problem. J. London Math. Soc. 40, 9–30, (1989).
[G] P. Gabriel. Unzerlegbare darstellungen I. Manuscripta Math. 6; 71–103. (1972).
[GEP] C. Geiss and J. A. de la Peña. Auslander-Reiten Components for Clans. To appear.
[DS] P. Dowbor and A. Skowronski. Galois corering of tame algebras. Arch. Math. 44; 522–529, (1985).
[H] D. Happel. On the derived category of a finite-dimensional algebras. Comment. Math. Helv. 62; 339–389, (1987).
[HW] D. Hughes and J. Waschbusch. Trivial extension of tilted algebras. Proc. London Math. Soc. 46; 347–364, (1983).
[Kr] H. Krause. Stable module categories and their representation type. Preprint Bielefeld. (1996).
[LDS] H. Lenzing, P. Dowbor and A. Skowronski. Galois covering of algebras by locally suppot-finite categories. Proceeding Letures Notes in Math. 1171, Springer (1986).
[NS] R. Norenberg and A. Skowronski. Tame minimal nonpolinomial growth strongly connected algebras. Proc. ICRA VII. CMS-AMS conference Proceeding Vol. 18; 519–538, (1996).
[N] C. Novoa-Bustos. Tipo de representacao e quiver ordinário do bimodulo DA. Tese de doutorado IME USP. (1999).
[P1] J.A. de la Peña. Algebras whose derived category is tame. Proceediings AMS-conference, Seattle (1997).
[P] J.A. de la Peña. On the representation type of one point extension of tame concealed algebras. Manuscripta Math., 61; 183– 194, (1988).
[R] C. M. Ringel. Tame algebras and quadratic form. Lectures Notes in Math. 1099, Springer,(1984).
[R2] C. M. Ringel. Tame algebras, on algorithms for solving vector space problems II. Proceedings Lecture Notes in Math. 831, Springer (1980).
[W] T. Wakamatsu. Stable equivalence between universal covers of trivial extension self-injective algebras. Tsukuba J. Math., 9; 299–316, (1985).
Published
2017-04-24
How to Cite
[1]
C. Novoa Bustos and J. A. de la Peña, “On the representation type of certain trivial extensions”, Proyecciones (Antofagasta, On line), vol. 20, no. 3, pp. 323-337, Apr. 2017.
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