00938nas a2200109 4500008004300000245007800043210006900121520056500190100001700755700002000772856003600792 2009 en_Ud 00aFamilies of Monads and Instantons from a Noncommutative ADHM Construction0 aFamilies of Monads and Instantons from a Noncommutative ADHM Con3 aWe give a \\\\theta-deformed version of the ADHM construction of SU(2) instantons with arbitrary topological charge on the sphere S^4. Classically the instanton gauge fields are constructed from suitable monad data; we show that in the deformed case the set of monads is itself a noncommutative space. We use these monads to construct noncommutative `families\\\' of SU(2) instantons on the deformed sphere S^4_\\\\theta. We also compute the topological charge of each of the families. Finally we discuss what it means for such families to be gauge equivalent.1 aBrain, Simon1 aLandi, Giovanni uhttp://hdl.handle.net/1963/347801246nas a2200121 4500008004100000245005100041210005100092260001800143520089000161100001701051700002001068856003601088 2004 en d00aFredholm modules for quantum euclidean spheres0 aFredholm modules for quantum euclidean spheres bSISSA Library3 aThe quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\\\\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which can be expressed in terms of a self-adjoint, unipotent matrix. We explicitly construct complete sets of generators for the K-theory (by nontrivial self-adjoint idempotents and unitaries) and the K-homology (by nontrivial Fredholm modules) of the spheres $S_q^{N-1}$. We also construct the corresponding Chern characters in cyclic homology and cohomology and compute the pairing of K-theory with K-homology. On odd spheres (i. e., for N even) we exhibit unbounded Fredholm modules by means of a natural unbounded operator D which, while failing to have compact resolvent, has bounded commutators with all elements in the algebra $A(S^{N-1}_q)$.1 aHawkins, Eli1 aLandi, Giovanni uhttp://hdl.handle.net/1963/163600369nas a2200109 4500008004100000245006100041210006100102260001800163100002000181700002300201856003500224 1985 en d00aFlat connections for Lax hierarchies on coadjoint orbits0 aFlat connections for Lax hierarchies on coadjoint orbits bSISSA Library1 aLandi, Giovanni1 aDe Filippo, Sergio uhttp://hdl.handle.net/1963/460