Noncommutative differential geometry and the structure of space time

1997 ◽  
pp. 17-42 ◽  
Author(s):  
Alain Connes
Keyword(s):  
Differential Geometry ◽  
Space Time ◽  
Noncommutative Differential Geometry

Noncommutative differential geometry on the quantum SU(2), I: An algebraic viewpoint

K-Theory ◽  
1990 ◽  
Vol 4 (2) ◽  
pp. 157-180 ◽  
Author(s):  
Tetsuya Masuda ◽  
Yoshiomi Nakagami ◽  
Junsei Watanabe
Keyword(s):  
Differential Geometry ◽  
Noncommutative Differential Geometry

Noncommutative differential geometry on the quantum two sphere of podleś. I: An algebraic viewpoint

K-Theory ◽  
1991 ◽  
Vol 5 (2) ◽  
pp. 151-175 ◽  
Author(s):  
Tetsuya Masuda ◽  
Yoshiomi Nakagami ◽  
Junsei Watanabe
Keyword(s):  
Differential Geometry ◽  
Noncommutative Differential Geometry

scholarly journals Algunos tipos especiales de determinantes en extensiones PBW torcidas graduadas

2021 ◽  
Vol 39 (1) ◽  
Author(s):  
Héctor Suárez ◽  
Duban Cáceres ◽  
Armando Reyes
Keyword(s):  
Differential Geometry ◽  
Algebraic Geometry ◽  
Regular Algebra ◽  
Noncommutative Algebraic Geometry ◽  
Noncommutative Differential Geometry ◽  
Regular Algebras ◽  
Skew Pbw Extensions ◽  
Finitely Presented

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)<x1, x2> 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.

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