Communications in Mathematical Physics

, Volume 221, Issue 1, pp 161–168

Instantons on the Quantum 4-pheres S4q

  • Ludwik Dąbrowski
  • Giovanni Landi
  • Tetsuya Masuda

DOI: 10.1007/PL00005572

Cite this article as:
Dąbrowski, L., Landi, G. & Masuda, T. Commun. Math. Phys. (2001) 221: 161. doi:10.1007/PL00005572

Abstract:

We introduce noncommutative algebras Aq of quantum 4-spheres S4q, with q∈ℝ, defined via a suspension of the quantum group SUq(2), and a quantum instanton bundle described by a selfadjoint idempotent e∈ Mat4(Aq), e2=e=e*. Contrary to what happens for the classical case or for the noncommutative instanton constructed in [8], the first Chern–Connes class ch1(e) does not vanish thus signaling a dimension drop. The second Chern–Connes class ch2(e) does not vanish as well and the couple (ch1(e), ch2(e) defines a cycle in the (b,B) bicomplex of cyclic homology.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Ludwik Dąbrowski
    • 1
  • Giovanni Landi
    • 2
  • Tetsuya Masuda
    • 3
  1. 1.Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014 Trieste, Italy.¶E-mail: dabrow@sissa.itIT
  2. 2.Dipartimento di Scienze Matematiche, Università di Trieste, Via Valerio 12/b, 34127, Trieste, Italy.¶E-mail: landi@dsm.univ.trieste.itIT
  3. 3.Institute of Mathematics, University of Tsukuba, Tsukuba 305, Japan.¶E-mail: tetsuya@math.tsukuba.ac.jpJP