Abstract:
We introduce noncommutative algebras A q of quantum 4-spheres S 4 q , with q∈ℝ, defined via a suspension of the quantum group SU q (2), and a quantum instanton bundle described by a selfadjoint idempotent e∈ Mat4(A q ), e 2=e=e *. Contrary to what happens for the classical case or for the noncommutative instanton constructed in [8], the first Chern–Connes class ch 1(e) does not vanish thus signaling a dimension drop. The second Chern–Connes class ch 2(e) does not vanish as well and the couple (ch 1(e), ch 2(e) defines a cycle in the (b,B) bicomplex of cyclic homology.
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Received: 12 December 2000 / Accepted: 10 March 2001
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Dąbrowski, L., Landi, G. & Masuda, T. Instantons on the Quantum 4-pheres S4q. Commun. Math. Phys. 221, 161–168 (2001). https://doi.org/10.1007/PL00005572
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DOI: https://doi.org/10.1007/PL00005572