Publications (2)2.97 Total impact
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ABSTRACT: We construct $\theta$deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative foursphere $S^4_\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\theta(2,H)$ by $Sp_\theta(2)$.International Mathematics Research Notices 11/2007; DOI:10.1093/imrn/rnn038 · 1.07 Impact Factor  [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 CMPCommunications in Mathematical Physics 07/2004; 263(1). DOI:10.1007/s0022000514943 · 1.90 Impact Factor
Publication Stats
28  Citations  
2.97  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
