Representations of nodal algebras of type~$\mathrm A$
Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 179-200.

Voir la notice de l'article provenant de la source Math-Net.Ru

We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type $\mathrm A$) we find a criterion of tameness.
Keywords: representations of finite dimensional algebras, gentle algebras, skewed-gentle algebras, inessential gluing.
Mots-clés : nodal algebras
@article{ADM_2013_15_2_a4,
     author = {Yu. Drozd and V. Zembyk},
     title = {Representations of nodal algebras of type~$\mathrm A$},
     journal = {Algebra and discrete mathematics},
     pages = {179--200},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a4/}
}
TY  - JOUR
AU  - Yu. Drozd
AU  - V. Zembyk
TI  - Representations of nodal algebras of type~$\mathrm A$
JO  - Algebra and discrete mathematics
PY  - 2013
SP  - 179
EP  - 200
VL  - 15
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a4/
LA  - en
ID  - ADM_2013_15_2_a4
ER  - 
%0 Journal Article
%A Yu. Drozd
%A V. Zembyk
%T Representations of nodal algebras of type~$\mathrm A$
%J Algebra and discrete mathematics
%D 2013
%P 179-200
%V 15
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a4/
%G en
%F ADM_2013_15_2_a4
Yu. Drozd; V. Zembyk. Representations of nodal algebras of type~$\mathrm A$. Algebra and discrete mathematics, Tome 15 (2013) no. 2, pp. 179-200. http://geodesic.mathdoc.fr/item/ADM_2013_15_2_a4/

[1] M. Auslander, I. Reiten, S. O. Smalø, Representation theory of Artin algebras, Cambridge University Press, 1995 | MR | Zbl

[2] V. Bekkert, E. N. Marcos, H. Merklen, “Indecomposables in derived categories of skewed-gentle algebras”, Commun. Algebra, 31 (2003), 2615–2654 | DOI | MR | Zbl

[3] I. Burban, Y. Drozd, “Derived categories of nodal algebras”, J. Algebra, 272 (2004), 46–94 | DOI | MR | Zbl

[4] Y. A. Drozd, “Finite modules over pure Noetherian algebras”, Trudy Mat. Inst. Steklov Acad. Sci. USSR, 183, 1990, 56–68 | MR | Zbl

[5] Y. Drozd, “Reduction algorithm and representations of boxes and algebras”, Comtes Rendue Math. Acad. Sci. Canada, 23 (2001), 97–125 | MR | Zbl

[6] Springer-Verlag, 1994 | MR | Zbl | Zbl

[7] C. Geiß, J. A. de la Peña, “Auslander-Reiten components for clans”, Bol. Soc. Mat. Mex., III Ser., 5:2 (1999), 307–326 | MR | Zbl

[8] M. M. Kleiner, “Partially ordered sets of finite type”, Zapiski Nauch. Semin. LOMI, 28, 1972, 32–41 | MR | Zbl

[9] M. M. Kleiner, “Pairs of partially ordered sets of tame representation type”, Linear Algebra Appl., 104 (1988), 103–115 | DOI | MR | Zbl

[10] L. A. Nazarova, “Partially ordered sets of infinite type”, Izv. Akad. Nauk SSSR, Ser. Mat., 39 (1975), 963–991 | MR

[11] L. A. Nazarova, A. V. Roiter, “Representations of partially ordered sets”, Zapiski Nauch. Semin. LOMI, 28, 1972, 5–31 | MR | Zbl

[12] A. Skowronski, J. Waschbusch, “Representation-finite biserial algebras”, J. Reine Angew. Math., 345 (1983), 172–181 | MR | Zbl

[13] D. E. Voloshyn, “Structure of nodal algebras”, Ukr. Mat. Zh., 63:7 (2011), 880–888 | DOI | MR | Zbl