Cyclic derivations, species realizations and potentials

López-Aguayo, Daniel; López-Aguayo, Daniel

doi:10.15446/recolma.v53nsupl.84083

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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.53 supl.1 Bogotá Dec. 2019 Epub Mar 24, 2020

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

Artículos originales

Cyclic derivations, species realizations and potentials

Derivaciones cíclicas, realización por especies y potenciales

Daniel López-Aguayo¹^*

^¹ Tecnologico de Monterrey, México

Abstract:

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.

Keywords: species realization; mutation; quiver with potential; strongly primitive

Resumen:

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.

Palabras clave: realización por especies; mutación; carcaj con potencial; fuertemente primitivo

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References

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

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

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

[4] 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. [ Links ]

[5] 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. [ Links ]

[6] 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. [ Links ]

[7] B. Nguefack, Potentials and Jacobian algebras for tensor algebras of bimodules, arXiv:1004.2213. [ Links ]

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

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

Received: June 05, 2018; Accepted: September 16, 2018

^*Correspondencia: Daniel López-Aguayo, Escuela de Ingeniería y Ciencias, Tecnologico de Monterrey, Monterrey, Nuevo León, México. Correo electrónico: dlopez.aguayo@itesm.mx. DOI: https://doi.org/10.15446/recolma.v53nsupl.84083

2010 Mathematics Subject Classification. 16G10, 16G20.

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