Instanton algebras and quantum 4-spheres

Details Instanton algebras and quantum 4-spheres Instanton algebras and quantum 4-spheres

2001-01-22

arxiv.org/abs/math/0101177v2

Differ.Geom.Appl. 16 (2002) 277-284

Mathematics

Quantum Algebra

10 pages. Minor changes; final version for the journal

Scientific paper

We study some generalized instanton algebras which are required to describe `instantonic complex rank 2 bundles'. The spaces on which the bundles are defined are not prescribed from the beginning but rather are obtained from some natural requirements on the instantons. They turn out to be quantum 4-spheres $S^4_q$, with $q\in\IC$, and the instantons are described by self-adjoint idempotents e. We shall also clarify some issues related to the vanishing of the first Chern-Connes class $ch_1(e)$ and on the use of the second Chern-Connes class $ch_2(e)$ as a volume form.

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