Open AccessAlgunos tipos especiales de determinantes en extensiones PBW torcidas graduadas
Author(s) -
Héctor Suárez,
Duban Cáceres,
Armando Reyes
Publication year - 2021
Publication title -
integración/revista integración, temas de matemáticas
Language(s) - English
Resource type - Journals
eISSN - 2145-8472
pISSN - 0120-419X
DOI - 10.18273/revint.v39n1-2021007
Subject(s) - mathematics , noncommutative geometry , automorphism , pure mathematics , skew , extension (predicate logic) , commutative property , differential (mechanical device) , connection (principal bundle) , algebra over a field , geometry , physics , astronomy , computer science , programming language , engineering , aerospace engineering
In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslander-regular algebra has trivial homological determinant. For A = σ(R) a graded skew PBW extension over a connected algebra R, we compute its P-determinant and the inverse of σ. In the particular case of quasi-commutative skew PBW extensions over Koszul Artin-Schelter regular algebras, we show explicitly the connection between the Nakayama automorphism of the ring of coefficients and the extension. Finally, we give conditions to guarantee that A is Calabi-Yau. We provide illustrative examples of the theory concerning algebras of interest in noncommutative algebraic geometry and noncommutative differential geometry.