Comparison between two differential graded algebras in noncommutative geometry

Proceedings of the Indian Academy of Sciences. Mathematical sciences

SATYAJIT GUIN^2¹  PARTHA SARATHI CHAKRABORTY^1² 

[1] Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur 208 016, India^2;Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India^1

关键词: Dirac differential graded algebra;    Connes’ calculus;    FGR differential graded algebra;    spectral triple;    quantum double suspension;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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 spinmanifolds, 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.

【 授权许可】

CC BY