Instantons on the Quantum 4-pheres S4q
- Cite this article as:
- Dąbrowski, L., Landi, G. & Masuda, T. Commun. Math. Phys. (2001) 221: 161. doi:10.1007/PL00005572
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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 , 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.