Comparison between two differential graded algebras in noncommutative geometry

被引：0
|
作者：
Partha Sarathi Chakraborty
Satyajit Guin
机构：
[1] Theoretical Statistics and Mathematics Unit,Department of Mathematics and Statistics
[2] Indian Statistical Institute,undefined
[3] Indian Institute of Technology,undefined
来源：
Proceedings - Mathematical Sciences | 2019年 / 129卷
关键词：
Dirac differential graded algebra; Connes’ calculus; FGR differential graded algebra; spectral triple; quantum double suspension; Primary: 58B34; Secondary: 46L87; 16E45;
D O I：
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摘要：
Starting with a spectral triple, one can associate two canonical differential graded algebras (DGA) defined by Connes (Noncommutative geometry (1994) Academic Press Inc., San Diego) and Fröhlich et al. (Comm. Math. Phys.203(1) (1999) 119–184). For the classical spectral triples associated with compact Riemannian spin manifolds, both these DGAs coincide with the de-Rham DGA. Therefore, both are candidates for the noncommutative space of differential forms. Here we compare these two DGAs in a very precise sense.
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