Some special types of determinants in graded skew P BW extensions.

Abstract

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) 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