Publications (2)3.19 Total impact
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ABSTRACT: We construct θdeformations of the classical groups SL(2, H) and Sp(2). Coacting on a basic instanton on a noncommutative foursphere S4 θ, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the Selfdual (and antiselfdual) solutions of Yang–Mills equations have played an important role both in mathematics and physics. Commonly called (anti)instantons, they are connections with selfdual curvature on smooth Gbundles over a four dimensional compact manifold M. In particular, one considers SU(2) instantons on the sphere S4.  [Show abstract] [Hide abstract]
ABSTRACT: We construct a quantum version of the SU(2) Hopf bundle $S^7 \to S^4$. The quantum sphere $S^7_q$ arises from the symplectic group $Sp_q(2)$ and a quantum 4sphere $S^4_q$ is obtained via a suitable selfadjoint idempotent $p$ whose entries generate the algebra $A(S^4_q)$ of polynomial functions over it. This projection determines a deformation of an (anti)instanton bundle over the classical sphere $S^4$. We compute the fundamental $K$homology class of $S^4_q$ and pair it with the class of $p$ in the $K$theory getting the value 1 for the topological charge. There is a right coaction of $SU_q(2)$ on $S^7_q$ such that the algebra $A(S^7_q)$ is a non trivial quantum principal bundle over $A(S^4_q)$ with structure quantum group $A(SU_q(2))$. Comment: 27 pages. Latex. v2 several substantial changes and improvements; to appear in CMP
Publication Stats
28  Citations  
3.19  Total Impact Points  
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Institutions

2007

IT University of Copenhagen
København, Capital Region, Denmark


2004

Scuola Internazionale Superiore di Studi Avanzati di Trieste
Trst, Friuli Venezia Giulia, Italy
