%0 Report
%D 2009
%T Families of Monads and Instantons from a Noncommutative ADHM Construction
%A Simon Brain
%A Giovanni Landi
%X We 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.
%G en_US
%U http://hdl.handle.net/1963/3478
%1 786
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-03T16:03:42Z\\nNo. of bitstreams: 1\\nBrain_Landi.pdf: 343656 bytes, checksum: 7d0ea754b63fce4b2a83db6423e67650 (MD5)
%0 Journal Article
%J J. Geom. Phys. 49 (2004) 272-293
%D 2004
%T Fredholm modules for quantum euclidean spheres
%A Eli Hawkins
%A Giovanni Landi
%X The 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 $A(S^{N-1}_q)$.
%B J. Geom. Phys. 49 (2004) 272-293
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/1636
%1 2482
%2 Mathematics
%3 Mathematical Physics
%$ Made available in DSpace on 2004-09-01T13:05:40Z (GMT). No. of bitstreams: 1\\nmath.KT0210139.pdf: 218018 bytes, checksum: 44f0c66ef47d8b2e1cafc955075c7626 (MD5)\\n Previous issue date: 2002
%R 10.1016/S0393-0440(03)00092-5
%0 Journal Article
%J Phys. Lett. A 108 (1985), no. 7, 311-314
%D 1985
%T Flat connections for Lax hierarchies on coadjoint orbits
%A Giovanni Landi
%A Sergio De Filippo
%B Phys. Lett. A 108 (1985), no. 7, 311-314
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/460
%1 3443
%2 Mathematics
%3 Mathematical Physics
%$ Made available in DSpace on 2004-09-01T12:32:42Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1985
%R 10.1016/0375-9601(85)90102-1