Instantons on the Quantum 4-Spheres S^4_q

Abstract

We introduce noncommutative algebras $A_q$ of quantum 4-spheres $S_q^4$, with $q\in\IR$, defined via a suspension of the quantum group $S{U}_q(2)$, and a quantum instanton bundle described by a selfadjoint idempotent $e\in \Mat_4(A_q)$, $e^2=e=e^{\ast }$. Contrary to what happens for the classical case or for the noncommutative instanton constructed in Connes-Landi, the first Chern-Connes class $c{h}_1(e)$ does not vanish thus signaling a dimension drop. The second Chern-Connes class $c{h}_2(e)$ does not vanish as well and the couple $(c{h}_1(e),c{h}_2(e))$ defines a cycle in the $(b,B)$ bicomplex of cyclic homology.

Minor changes. To appear in CMP

References in corpus (1)

• Instanton algebras and quantum 4-spheres

Cited by in corpus (14)

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• Quantum even spheres Sigma_q^2n from Poisson double suspension
• q-Deformed su(2) instantons by q-quaternions
• q-Quaternions and q-deformed su(2) instantons
• Differential and Twistor Geometry of the Quantum Hopf Fibration
• Finitely-Generated Projective Modules over the Theta-deformed 4-sphere
• Noncommutative Spheres and Instantons
• q-Deformed quaternions and su(2) instantons
• Twisted Configurations over Quantum Euclidean Spheres
• Dirac operator on the quantum fuzzy four-sphere $S_{qF}^4$