Instantons on the Quantum 4-Spheres S4q
Ludwik Dabrowski, Giovanni Landi, Tetsuya Masuda
Abstract
We introduce noncommutative algebras Aq of quantum 4-spheres S4q, with q∈, defined via a suspension of the quantum group SUq(2), and a quantum instanton bundle described by a selfadjoint idempotent e∈ 4(Aq), e2=e=e*. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, 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.
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