2009/03/13 by Paolo Aschieri, P. Aschieri · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Operator Algebra Research #Noncommutative and Quantum Gravity Theories #math.QA
paper · pdf · doi:10.1134/s1061920809030054
published as Russ. J. Math. Phys., 16, No. 3 (2009) 371 · 27 pages. Based on the talk presented at the conference "Geometry and Operators Theory," Ancona (Italy), September 2007
arxiv created 2009/03/13 · openalex publication_date 2009/09/01 · arxiv updated 2010/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 ⋆-Poisson brackets to ⋆-commutators).