Revista Integración, temas de matemáticas.
Vol. 39 Núm. 1 (2021): Revista integración, temas de matemáticas
Artículos científicos

Algunos tipos especiales de determinantes en extensiones P BW torcidas graduadas.

Héctor Suárez
Universidad Pedagógica y Tecnológica de Colombia
Duban Cáceres
Universidad Pedagógica y Tecnológica de Colombia
Armando Reyes
Universidad Nacional de Colombia.

Publicado 2021-05-19

Palabras clave

  • Álgebra Calabi-Yau,
  • extensión PBW torcida,
  • extensión de Ore doble,
  • determinante homológico,
  • P-determinante,
  • automorfismo de Nakayama
  • ...Más
    Menos

Cómo citar

Suárez, H., Cáceres, D., & Reyes, A. (2021). Algunos tipos especiales de determinantes en extensiones P BW torcidas graduadas. Revista Integración, Temas De matemáticas, 39(1), 91–107. https://doi.org/10.18273/revint.v39n1-2021007

Resumen

En este artículo, demostramos que el automorfismo de Nakayama de una extensión PBW torcida graduada sobre un álgebra de Koszul finitamente presentada y Auslander-regular tiene determinante homológico trivial. Para A = σ(R)<x1, x2> una extensión PBW torcida graduada sobre un álgebra conexa R, calculamos su P-determinante y el inverso de σ. En el caso particular de extensiones PBW torcidas cuasi-conmutativas sobre álgebras de Koszul Artin-Schelter regulares, mostramos explícitamente la relación entre el automorfismo de Nakayama del anillo de coeficientes y la extensión. Finalmente, damos condiciones para garantizar que A sea Calabi-Yau. Proporcionamos ejemplos ilustrativos de la teoría con álgebras de interés en geometría algebraica no conmutativa y geometría diferencial no conmutativa.

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