TY - JOUR
T1 - Noncommutative circle bundles and new Dirac operators
JF - Communications in Mathematical Physics. Volume 318, Issue 1, 2013, Pages 111-130
Y1 - 2013
A1 - Ludwik Dabrowski
A1 - Andrzej Sitarz
KW - Quantum principal bundles
AB - We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.
PB - Springer
UR - http://hdl.handle.net/1963/7384
N1 - This article is composed of 25 pages and is recorded in PDF format
U1 - 7432
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -
TY - JOUR
T1 - The Noncommutative Geometry of the Quantum Projective Plane
JF - Rev. Math. Phys. 20 (2008) 979-1006
Y1 - 2008
A1 - Francesco D'Andrea
A1 - Ludwik Dabrowski
A1 - Giovanni Landi
AB - We study the spectral geometry of the quantum projective plane CP^2_q. In particular, we construct a Dirac operator which gives a 0^+ summable triple, equivariant under U_q(su(3)).
UR - http://hdl.handle.net/1963/2548
U1 - 1571
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - JOUR
T1 - Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces
JF - Mod. Phys. Lett. A 18 (2003) 2371-2379
Y1 - 2003
A1 - Ludwik Dabrowski
A1 - Thomas Krajewski
A1 - Giovanni Landi
AB - We study sigma-models on noncommutative spaces, notably on noncommutative tori. We construct instanton solutions carrying a nontrivial topological charge q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons is conjectured to consists of an ordinary torus endowed with a complex structure times a projective space $CP^{q-1}$.
PB - World Scientific
UR - http://hdl.handle.net/1963/3215
U1 - 1086
U2 - Mathematics
U3 - Mathematical Physics
ER -