TY - RPRT
T1 - Families of Monads and Instantons from a Noncommutative ADHM Construction
Y1 - 2009
A1 - Simon Brain
A1 - Giovanni Landi
AB - 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.
UR - http://hdl.handle.net/1963/3478
U1 - 786
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Fredholm modules for quantum euclidean spheres
JF - J. Geom. Phys. 49 (2004) 272-293
Y1 - 2004
A1 - Eli Hawkins
A1 - Giovanni Landi
AB - 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 $A(S^{N-1}_q)$.
PB - SISSA Library
UR - http://hdl.handle.net/1963/1636
U1 - 2482
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Flat connections for Lax hierarchies on coadjoint orbits
JF - Phys. Lett. A 108 (1985), no. 7, 311-314
Y1 - 1985
A1 - Giovanni Landi
A1 - Sergio De Filippo
PB - SISSA Library
UR - http://hdl.handle.net/1963/460
U1 - 3443
U2 - Mathematics
U3 - Mathematical Physics
ER -