00746nas a2200145 4500008004300000245004200043210004200085260002800127520032600155100002000481700001900501700001800520700002600538856003600564 2008 en_Ud 00aNoncommutative families of instantons0 aNoncommutative families of instantons bOxford University Press3 aWe construct $\\\\theta$-deformations of the classical groups SL(2,H) and Sp(2). Coacting on the basic instanton on a noncommutative four-sphere $S^4_\\\\theta$, we construct a noncommutative family of instantons of charge 1. The family is parametrized by the quantum quotient of $SL_\\\\theta(2,H)$ by $Sp_\\\\theta(2)$.1 aLandi, Giovanni1 aPagani, Chiara1 aReina, Cesare1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/341701006nas a2200157 4500008004100000245003400041210002700075260001300102520058600115100002200701700002000723700002000743700002600763700002300789856003600812 2005 en d00aThe Dirac operator on SU_q(2)0 aDirac operator on SUq2 bSpringer3 aWe construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the
spectrum of the operator D is the same as that of the usual Dirac operator on
the 3-dimensional round sphere. The presence of an equivariant real structure J
demands a modification in the axiomatic framework of spectral geometry, whereby the commutant and first-order properties need be satisfied only modulo infinitesimals of arbitrary high order.1 aDabrowski, Ludwik1 aLandi, Giovanni1 aSitarz, Andrzej1 avan Suijlekom, Walter1 aVarilly, Joseph C. uhttp://hdl.handle.net/1963/442500687nas a2200145 4500008004300000245003900043210003300082520027900115100002600394700002200420700002000442700002000462700002300482856003600505 2005 en_Ud 00aThe local index formula for SUq(2)0 alocal index formula for SUq23 aWe discuss the local index formula of Connes-Moscovici for the isospectral noncommutative geometry that we have recently constructed on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.1 avan Suijlekom, Walter1 aDabrowski, Ludwik1 aLandi, Giovanni1 aSitarz, Andrzej1 aVarilly, Joseph C. uhttp://hdl.handle.net/1963/171300942nas a2200109 4500008004300000245005300043210005300096520060100149100002000750700002600770856003600796 2005 en_Ud 00aPrincipal fibrations from noncommutative spheres0 aPrincipal fibrations from noncommutative spheres3 aWe construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.1 aLandi, Giovanni1 avan Suijlekom, Walter uhttp://hdl.handle.net/1963/2284