Skip to main content
Log in

Comparison between two differential graded algebras in noncommutative geometry

  • Published:
Proceedings - Mathematical Sciences Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. Bertozzini P, Conti R and Lewkeeratiyutkul W, A category of spectral triples and discrete groups with length function, Osaka J. Math. 43(2) (2006) 327–350

    MathSciNet  MATH  Google Scholar 

  2. Chakraborty P S and Guin S, Connes’ calculus for the quantum double suspension, J. Geom. Phys. 88 (2015) 16–29

    Article  MathSciNet  Google Scholar 

  3. Chakraborty P S and Pal A, Spectral triples and associated Connes–de Rham complex for the quantum SU(2) and the quantum sphere, Comm. Math. Phys. 240(3) (2003) 447–456

    Article  MathSciNet  Google Scholar 

  4. Chakraborty P S and Sundar S, Quantum double suspension and spectral triples, J. Funct. Anal. 260(9) (2011) 2716–2741

    Article  MathSciNet  Google Scholar 

  5. Connes A, Noncommutative geometry (1994) (San Diego, CA: Academic Press Inc.)

  6. Connes A and Moscovici H, The local index formula in noncommutative geometry, Geom. Funct. Anal. 5(2) (1995) 174–243

    Article  MathSciNet  Google Scholar 

  7. Fröhlich J, Grandjean O and Recknagel A, Supersymmetric quantum theory and non-commutative geometry, Comm. Math. Phys. 203(1) (1999) 119–184

    Article  MathSciNet  Google Scholar 

  8. Hong J H and Szymański W, Quantum spheres and projective spaces as graph algebra, Comm. Math. Phys. 232(1) (2002) 157–188

    Article  MathSciNet  Google Scholar 

  9. Hong J H and Szymański W, Noncommutative balls and mirror quantum spheres, J. London Math. Soc. 77(3) (2008) 607–626

    Article  MathSciNet  Google Scholar 

  10. Sukochev F and Zanin D, \(\zeta \)-function and heat kernel formulae, J. Funct. Anal. 260(8) (2011) 2451–2482

    Article  MathSciNet  Google Scholar 

Download references


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).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Satyajit Guin.

Additional information

Communicated by B V Rajarama Bhat.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chakraborty, P.S., Guin, S. Comparison between two differential graded algebras in noncommutative geometry. Proc Math Sci 129, 29 (2019).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI:


2010 Mathematics Subject Classification