TY - JOUR
T1 - Star product geometries
AU - Aschieri, P.
N1 - Funding Information:
I felt very honored to present this work at the celebration of the 65th birthday of Nicolae Teleman. This research is based on joint work with Marija Dimitriević, Frank Meyer, Julius Wess and with Fedele Lizzi, Patrizia Vitale; I would like to thank them for the fruitful collaboration. A partial support from the European Community’s Human Potential Program under contract MRTN-CT-2004-005104 and from the Italian MIUR under contract PRIN-2005023102 is acknowledged.
PY - 2009/9
Y1 - 2009/9
N2 - We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows us to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. Principles of symmetry can be implemented in this way. Two examples are considered: (a) the general covariance in noncommutative spacetime, which leads to a noncommutative theory of gravity, and b) symplectomorphims of the algebra of observables associated with noncommutative configuration spaces, which leads to a geometric formulation of quantization on noncommutative spacetime (i.e., we establish a noncommutative correspondence principle from {star operator}-Poisson brackets to {star operator}-commutators).
AB - We consider noncommutative geometries obtained from a triangular Drinfeld twist. This allows us to construct and study a wide class of noncommutative manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms. Principles of symmetry can be implemented in this way. Two examples are considered: (a) the general covariance in noncommutative spacetime, which leads to a noncommutative theory of gravity, and b) symplectomorphims of the algebra of observables associated with noncommutative configuration spaces, which leads to a geometric formulation of quantization on noncommutative spacetime (i.e., we establish a noncommutative correspondence principle from {star operator}-Poisson brackets to {star operator}-commutators).
UR - http://www.scopus.com/inward/record.url?scp=71249088337&partnerID=8YFLogxK
U2 - 10.1134/S1061920809030054
DO - 10.1134/S1061920809030054
M3 - Article
SN - 1061-9208
VL - 16
SP - 371
EP - 383
JO - Russian Journal of Mathematical Physics
JF - Russian Journal of Mathematical Physics
IS - 3
ER -