Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
El "unravelling" para bigráficas diferenciales
PDF (Español (España))

Keywords

representation
differential bigraphic
‘unravelling’
quadratic form
equivalence
representación
bigráfica diferencial
‘unravelling’
forma cuadrática
equivalencia

How to Cite

Boza Cordero, J. (1998). El "unravelling" para bigráficas diferenciales. Revista De Matemática: Teoría Y Aplicaciones, 5(1), 25–37. https://doi.org/10.15517/rmta.v5i1.152

Abstract

Here are examined the main properties of the algorithm called ¨unravelling¨ for differential  bigraphs. This algorithm was originally developed for differential graded categories and was useful in the proof the celebrated ¨tame-wild¨ theorem of ¨Drozd´s. First we describe the algorithm, and then we establish in detail the existence of an equivalence between certain subcategories of representations of the original and the derived bigraphs. We also exhibit the precise behaviour of the norm and the quadratic form under the algorithm.


https://doi.org/10.15517/rmta.v5i1.152
PDF (Español (España))

References

[ARS] Auslander, M.; Reiten, I.; Smalo, S. (1995) Representation Theory of Artin Algebras. Cambridge Univ. Press, Cambridge.

[BCS] Bautista, R.; Colavita, L.; Salmerón, L. (1981) “On Adjoint Funtors in Representation Theory”, in Representations of Algebras, Lecture Notes in Mathematics 903, Springer-Verlag: 9–25.

[BK] Bautista, R.; Kleiner, M. (1990) “Almost split sequences for relatively projective modules”, J. Algebra 135: 19–56.

[BB] Bautista, R.; Boza, J. (1996) “Reduction algorithms and quadratic forms”, Public. Prelim. no. ,Inst. Mat., UNAM, México.

[Bo1] Boza, J. (1996)Algoritmos de Reducción en la Teoría de Representaciones de Coálgebras. Tesis doctoral, UNAM, México.

[Bo2] Boza, J. (1997) “Algoritmos de reducción para bigráficas diferenciales”, Revista de Matemática: Teora y Aplicaciones 4(2): 24–42.

[BZ] Bautista, R.; Zuazúa, R. (1996) “Morita equivalence and reduction algorithms for representations of coalgebras”, Canadian Math. Soc., Conference Proc.18: 51–80.

[CB1] Crawley-Boevey, W.W. (1988) “On tame algebras and bocses”, Proc. London Math. Soc. 56(3): 451–483.

[CB2] Crawley-Boevey, W.W. (1992) “Modules of finite length over their endomorphismrings”, in Representations of Algebras and Related Topics, Cambridge Univ. Press, No. 168: 127–184.

[CB3] Crawley-Boevey, W.W. “Matrix reductions for Artinian rings, and an application to rings of finite representation type’, Journal of Algebra 157(1): 1–25.

[CB4] Crawley-Boevey, W.W. (1990) Matrix problems and Drozd’s Theorem. Topics in Algebra, Banach Center Publ. Warzaw: 199–222.

[D1] Drozd, Y.A. (1980) “Tame and wild matrix problems”, in Representation Theory II, Lecture Notes in Mathematics 832, Springer-Verlag: 242–258.

[D2] Drozd, Y.A. (1986) “Tame and wild matrix problems”, Amer. Math. Soc. Transl. 128(2): 31–55.

[K] Kleiner, M. (1984) “Matrix problems and representations of finite dimensional algebras”, Proceed. IV-ICRA, Carleton Univ., Ottawa.

[La] Lakatos, I. (1994) Pruebas y Refutaciones. La Lógica del Descubrimiento Matemático. Alianza Universidad, Madrid.

[MacL] MacLane, S. (1988) “Categories for the Working Mathematician”. Springer-Verlag.

[Ma] Maltsev, A.I. (1978)Fundamentos de Álgebra Lineal. Mir, Moscú.

[M] Montaño, G. (1993) “Caracterización de bocses de dimensión finita de tipo manso”. Tesis de Maestría, UNAM, México.

[O] Ovsienko, S.A. (1993) “Generic representations of free bocses”, Preprint 93-03, Universität Bielefeld, 28 p.

[Ri] Ringel, C.M. (1984)Tame Algebras and Integral Quadratic Forms. Lecture Notes in Mathematics, 1099, Springer-Verlag.

[Ro] Roiter, A.V. (1980) “Matrix problems and representations of bocs’s”, in Lecture Notes in Mathematics 831, Springer-Verlag: 288–324.

[RK] Roiter, A.V.; Kleiner, M. “Representations of differential graded categories”, in Lecture Notes in Mathematics 488, Springer-Verlag: 316–339.

[S] Simson, D. (1992) “Linear representations of partially ordered sets and vector space categories”, Gordon and Breach, Switzerland.

Comments

Downloads

Download data is not yet available.