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Comparison between two differential graded algebras in noncommutative geometry

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Abstract

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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Acknowledgements

The first author (PSC) acknowledges support of DST, India through Swarnajayanti Fellowship Award Project No. DST/SJF/MSA-01/2012-13 and the second author (SG) acknowledges support of DST, India through INSPIRE Faculty Award (Award No. DST/INSPIRE/04/2015/000901).

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Authors and Affiliations

  1. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata, 700 108, India

    Partha Sarathi Chakraborty

  2. Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, 208 016, India

    Satyajit Guin

Authors
  1. Partha Sarathi Chakraborty
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  2. Satyajit Guin
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Correspondence to Satyajit Guin.

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Communicated by B V Rajarama Bhat.

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Chakraborty, P.S., Guin, S. Comparison between two differential graded algebras in noncommutative geometry. Proc Math Sci 129, 29 (2019). https://doi.org/10.1007/s12044-019-0467-y

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  • DOI: https://doi.org/10.1007/s12044-019-0467-y

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