TY - JOUR
T1 - Instantons on the Quantum 4-Spheres S^4_q
JF - Comm. Math. Phys. 221 (2001) 161-168
Y1 - 2001
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
A1 - Tetsuya Masuda
AB - We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S^4_q$, with $q\\\\in\\\\IR$, defined via a suspension of the quantum group $SU_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\\\\in \\\\Mat_4(A_q)$, $e^2=e=e^*$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, 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.
PB - Springer
UR - http://hdl.handle.net/1963/3135
U1 - 1198
U2 - Mathematics
U3 - Mathematical Physics
ER -