Calabi-Yau property for graded skew PBW extensions

Héctor Suárez; Oswaldo Lezama; Armando Reyes

doi:10.15446/recolma.v51n2.70902

Publicado

2017-07-01

Calabi-Yau property for graded skew PBW extensions

Propiedad Calabi-Yau para extensiones PBW torcidas graduadas

DOI:

https://doi.org/10.15446/recolma.v51n2.70902

Palabras clave:

Graded skew PBW extensions, AS-regular algebras, skew Calabi-Yau algebras (en)
Extensiones PBW torcidas graduadas, álgebras AS-regular, álgebras Calabi-Yau torcidas (es)

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Autores/as

Héctor Suárez Universidad Nacional de Colombia y Universidad Pedagógica y Tecnológica de Colombia
Oswaldo Lezama Universidad Nacional de Colombia
Armando Reyes Universidad Nacional de Colombia

Resumen (en)
Resumen (es)

Graded skew PBW extensions were defined by the first author as a generalization of graded iterated Ore extensions [36]. The purpose of this paper is to study the Artin-Schelter regularity and the (skew) Calabi-Yau condition for this kind of extensions. We prove that every graded quasi-commutative skew PBW extension of an Artin-Schelter regular algebra is also an Artin-Schelter regular algebra and, as a consequence, every graded quasi-commutative skew PBW extension of a connected skew Calabi-Yau algebra is skew Calabi-Yau. Finally, we prove that graded skew PBW extensions of a finitely presented connected Auslander-regular algebra are skew Calabi-Yau.

Las extensiones PBW torcidas graduadas fueron definidas por el primer autor como una generalización de las extensiones de Ore iteradas graduadas [36]. El propósito de este artículo es estudiar las condiciones Artin-Schelter regular y Calabi-Yau (torcida) para esta clase de extensiones. Demostramos que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra Artin-Schelter regular también es Artin-Schelter regular, y, como consecuencia, que cada extensión PBW torcida cuasi-conmutativa graduada de un álgebra conexa Calabi-Yau torcida es Calabi-Yau torcida. Finalmente, mostramos que las extensiones PBW torcidas graduadas de álgebras Auslander-regular finitamente presentadas y conexas son Calabi-Yau torcidas.

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Cómo citar

APA

Suárez, H., Lezama, O. y Reyes, A. (2017). Calabi-Yau property for graded skew PBW extensions. Revista Colombiana de Matemáticas, 51(2), 221–239. https://doi.org/10.15446/recolma.v51n2.70902

ACM

[1]

Suárez, H., Lezama, O. y Reyes, A. 2017. Calabi-Yau property for graded skew PBW extensions. Revista Colombiana de Matemáticas. 51, 2 (jul. 2017), 221–239. DOI:https://doi.org/10.15446/recolma.v51n2.70902.

ACS

(1)

Suárez, H.; Lezama, O.; Reyes, A. Calabi-Yau property for graded skew PBW extensions. rev.colomb.mat 2017, 51, 221-239.

ABNT

SUÁREZ, H.; LEZAMA, O.; REYES, A. Calabi-Yau property for graded skew PBW extensions. Revista Colombiana de Matemáticas, [S. l.], v. 51, n. 2, p. 221–239, 2017. DOI: 10.15446/recolma.v51n2.70902. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/70902. Acesso em: 15 may. 2024.

Chicago

Suárez, Héctor, Oswaldo Lezama, y Armando Reyes. 2017. «Calabi-Yau property for graded skew PBW extensions». Revista Colombiana De Matemáticas 51 (2):221-39. https://doi.org/10.15446/recolma.v51n2.70902.

Harvard

Suárez, H., Lezama, O. y Reyes, A. (2017) «Calabi-Yau property for graded skew PBW extensions», Revista Colombiana de Matemáticas, 51(2), pp. 221–239. doi: 10.15446/recolma.v51n2.70902.

IEEE

[1]

H. Suárez, O. Lezama, y A. Reyes, «Calabi-Yau property for graded skew PBW extensions», rev.colomb.mat, vol. 51, n.º 2, pp. 221–239, jul. 2017.

MLA

Suárez, H., O. Lezama, y A. Reyes. «Calabi-Yau property for graded skew PBW extensions». Revista Colombiana de Matemáticas, vol. 51, n.º 2, julio de 2017, pp. 221-39, doi:10.15446/recolma.v51n2.70902.

Turabian

Suárez, Héctor, Oswaldo Lezama, y Armando Reyes. «Calabi-Yau property for graded skew PBW extensions». Revista Colombiana de Matemáticas 51, no. 2 (julio 1, 2017): 221–239. Accedido mayo 15, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/70902.

Vancouver

1.

Suárez H, Lezama O, Reyes A. Calabi-Yau property for graded skew PBW extensions. rev.colomb.mat [Internet]. 1 de julio de 2017 [citado 15 de mayo de 2024];51(2):221-39. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/70902

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