A note on the fundamental group of a one-point extension
DOI:
https://doi.org/10.4067/S0716-09172005000100007Keywords:
Fundamental groups, Bound quivers, Presentations of algebras.Abstract
In this note, we consider an algebra A which is a one-point extension of another algebra B and we study the morphism of fundamental groups induced by the inclusion of (the bound quiver of ) B into (that of ) A. Our main result says that the cokernel of this morphism is a free group and we prove some consequences from this fact.
References
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[2] I. Assem and J.A. de la Peña. The fundamental groups of a triangular algebra. Comm. Algebra, 24 (1) : pp. 187—208, (1996).
[3] K. Bongartz and P. Gabriel. Covering spaces in representation theory. Invent. Math, 65 (3) : pp. 331—378, (1981)-(1982).
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[5] J. C. Bustamante. On the fundamental group of a schurian algebra. Comm. Algebra, 30 (11) : pp. 5305—5327, (2002).
[6] J. C. Bustamante. The classifying space of a bound quiver. J. Algebra, 277 : pp. 431—455, (2004).
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[2] I. Assem and J.A. de la Peña. The fundamental groups of a triangular algebra. Comm. Algebra, 24 (1) : pp. 187—208, (1996).
[3] K. Bongartz and P. Gabriel. Covering spaces in representation theory. Invent. Math, 65 (3) : pp. 331—378, (1981)-(1982).
[4] M. J. Bardzell and E. N. Marcos. H1(?) and presentations of finite dimensional algebras. Number 224 in Lecture Notes in Pure and Applied Mathematics, pages 31—38. Marcel Dekker, (2001).
[5] J. C. Bustamante. On the fundamental group of a schurian algebra. Comm. Algebra, 30 (11) : pp. 5305—5327, (2002).
[6] J. C. Bustamante. The classifying space of a bound quiver. J. Algebra, 277 : pp. 431—455, (2004).
[7] R. Martínez-Villa and J.A. de la Peña. The universal cover of a quiver with relations. J. Pure Appl. Algebra, 30 : pp. 873—887, (1983).
[8] A. Skowronski. Simply connected algebras and Hochschild cohomologies. In Proceedings of the sixth international conference on representation of algebras, number 14 in Ottawa-Carleton Math. Lecture Notes Ser., pp. 431—448, Ottawa, ON, (1992).
Published
2017-04-20
How to Cite
[1]
I. Assem, J. C. Bustamante, D. Castonguay, and C. Novoa Bustos, “A note on the fundamental group of a one-point extension”, Proyecciones (Antofagasta, On line), vol. 24, no. 1, pp. 79-87, Apr. 2017.
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