Publicado

2017-07-01

Calabi-Yau property for graded skew PBW extensions

Propiedad Calabi-Yau para extensiones PBW torcidas graduadas

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
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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Derechos de autor 2017 Revista Colombiana de Matemáticas

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Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.