Quivers of Bound Path Algebras and Bound Path Coalgebras
AbstractAlgebras and coalgebras can be represented as quiver (directed graph), and from quiver we can construct algebras and coalgebras called path algebras and path coalgebras. In this paper we show that the quiver of a bound path coalgebra (resp. algebra) is the dual quiver of its bound path algebra (resp. coalgebra).
Assem, I., Simson, D. & Si Skowronski, A., Elements of the Representation Theory of Associative Algebras 1, London Mathematical Society Student Texts 65, Cambridge University Press, 2006.
Muchtadi-Alamsyah, I. Algebras and quivers, Proceeding ISSM Paris, 2005.
Chin, W., A brief introduction to coalgebra representation theory, in Hopf Algebra, Lecture Notes in Pure and Appl.Math, 237, pp.109-131, Marcel Dekker, New York, 2004.
Auslander, M., Reiten, I. & Smaloe, S.O., Representation Theory of Artin Algebras, Cambridge Univ Press, 1995.
Chin, W., Si Montgomery, S., Basic Coalgebras, Modular interfaces (Reverside, CA, 1995), 41-47, AMS/IP Stud. Adv. Math. 4, Providence, RI:Amer.Math.Soc., 1997.
Muchtadi-Alamsyah, I. & Garminia,H. Quivers of Path Algebras and Path Coalgebras, Proceeding IndoMS International Conference on Mathematics and Its Applications, 2009.
Woodcock, D. Some categorical remarks on the representation theory of coalgebras, Communication in Algebra, 25, pp. 2775-2794, 1997.
Simson, D. Path coalgebras of quivers with relations and a tame-wild dichotomy problem for coalgebras, Lecture Notes in Pure and Applied Mathematics, 236, pp. 465-492, 2005.
Jara, P., Merino, L.M. & Navarro, G. On Path Coalgebras of Quivers with Relations, Colloq. Math., 102, pp. 49-65, 2005.
Abe, E., Hopf Algebras, Cambridge University Press 1977.