Abstract

SUAREZ, Héctor; CACERES, Duban  and  REYES, Armando. Some special types of determinants in graded skew PBW extensions. Integración - UIS [online]. 2021, vol.39, n.1, pp.91-107.  Epub Feb 28, 2021. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n1-2021007.

In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslanderregular algebra has trivial homological determinant. For A = σ(R) {x1, x2} a graded skew PBW extension over a connected algebra R, we compute its Pdeterminant 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.

Keywords : Calabi-Yau algebra; skew PBW extension; double Ore extension; homological determinant; P-determinant; Nakayama automorphism; MSC2010: 16S37; 16W50; 16W70; 16S36; 13N10.

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