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.

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.

Palabras clave: Álgebra Calabi-Yau, extensión PBW torcida, extensión de Ore doble, determinante homológico, P-determinante, automorfismo de Nakayama

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Publicado
2021-05-19