Cyclic derivations, species realizations and potentials

Daniel López-Aguayo

doi:10.15446/recolma.v53nsupl.84083

Publicado

2019-12-11

Cyclic derivations, species realizations and potentials

Derivaciones cíclicas, realización por especies y potenciales

DOI:

https://doi.org/10.15446/recolma.v53nsupl.84083

Palabras clave:

species realization, mutation, quiver with potential, strongly primitive (en)
realización por especies, mutación, carcaj con potencial, fuertemente primitivo (es)

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Autores/as

Daniel López-Aguayo Tecnológico de Monterrey

Resumen (en)
Resumen (es)

In this paper we give an overview of a generalization, introduced by R. Bautista and the author, of the theory of mutation of quivers with potential developed in 2007 by Derksen-Weyman-Zelevinsky. This new construction allows us to consider finite dimensional semisimple F-algebras, where F is any field. We give a brief account of the results concerning this generalization and its main consequences.

En este artículo daremos un panorama de una generalización, introducida por R. Bautista y el autor, de la teoría de mutación de carcajes con potencial desarrollada en 2007 por Derksen-Weyman-Zelevinsky. Esta nueva construcción nos permite considerar álgebras semisimples de dimensión finita sobre F, donde F es cualquier campo. Daremos un resumen de los resultados de esta generalización y de sus principales consecuencias.

Referencias

D. López-Aguayo (2018), A note on species realizations and nondegeneracy of potentials, Journal of Algebra and Its Applications 18 (2019), no. 2.

R. Bautista and D. López-Aguayo, Potentials for some tensor algebras, arXiv:1506.05880.

L. Demonet, Mutations of group species with potentials and their representations. Applications to cluster algebras, arXiv:1003.5078.

H. Derksen, J. Weyman, and A. Zelevinsky, Quivers with potentials and their representations I: Mutations, Selecta Math. 14 (2008), no. 1, 59-119, arXiv:0704.0649.

J. Geuenich and D. Labardini-Fragoso, Species with potential arising from surfaces with orbifold points of order 2, Part I: one choice of weights, Mathematische Zeitschrift 286 (2017), no. 3-4, 1065-1143, arXiv:1507.04304.

D. Labardini-Fragoso and A. Zelevinsky, Strongly primitive species with potentials I: Mutations, Boletín de la Sociedad Matemática Mexicana (Third series) 22 (2016), no. 1, 47-115, arXiv:1306.3495.

B. Nguefack, Potentials and Jacobian algebras for tensor algebras of bimodules, arXiv:1004.2213.

S. Roman, Field theory, Graduate Texts in Mathematics, 158. Springer-Verlag New York, 2006.

G.-C. Rota, B. Sagan, and P. R. Stein, A cyclic derivative in noncommutative algebra, Journal of Algebra 64 (1980), 54-75.

Cómo citar

APA

López-Aguayo, D. (2019). Cyclic derivations, species realizations and potentials. Revista Colombiana de Matemáticas, 53(supl), 185–194. https://doi.org/10.15446/recolma.v53nsupl.84083

ACM

[1]

López-Aguayo, D. 2019. Cyclic derivations, species realizations and potentials. Revista Colombiana de Matemáticas. 53, supl (dic. 2019), 185–194. DOI:https://doi.org/10.15446/recolma.v53nsupl.84083.

ACS

(1)

López-Aguayo, D. Cyclic derivations, species realizations and potentials. rev.colomb.mat 2019, 53, 185-194.

ABNT

LÓPEZ-AGUAYO, D. Cyclic derivations, species realizations and potentials. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. supl, p. 185–194, 2019. DOI: 10.15446/recolma.v53nsupl.84083. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/84083. Acesso em: 27 dic. 2025.

Chicago

López-Aguayo, Daniel. 2019. «Cyclic derivations, species realizations and potentials». Revista Colombiana De Matemáticas 53 (supl):185-94. https://doi.org/10.15446/recolma.v53nsupl.84083.

Harvard

López-Aguayo, D. (2019) «Cyclic derivations, species realizations and potentials», Revista Colombiana de Matemáticas, 53(supl), pp. 185–194. doi: 10.15446/recolma.v53nsupl.84083.

IEEE

[1]

D. López-Aguayo, «Cyclic derivations, species realizations and potentials», rev.colomb.mat, vol. 53, n.º supl, pp. 185–194, dic. 2019.

MLA

López-Aguayo, D. «Cyclic derivations, species realizations and potentials». Revista Colombiana de Matemáticas, vol. 53, n.º supl, diciembre de 2019, pp. 185-94, doi:10.15446/recolma.v53nsupl.84083.

Turabian

López-Aguayo, Daniel. «Cyclic derivations, species realizations and potentials». Revista Colombiana de Matemáticas 53, no. supl (diciembre 11, 2019): 185–194. Accedido diciembre 27, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/84083.

Vancouver

1.

López-Aguayo D. Cyclic derivations, species realizations and potentials. rev.colomb.mat [Internet]. 11 de diciembre de 2019 [citado 27 de diciembre de 2025];53(supl):185-94. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/84083

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CrossRef Cited-by

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1. Raphael Bennett-Tennenhaus, Daniel Labardini-Fragoso. (2025). Semilinear clannish algebras arising from surfaces with orbifold points. Annals of Representation Theory, 2(4), p.439. https://doi.org/10.5802/art.32.