On the existence of star products on quotient spaces of linear Hamiltonian torus actions - Danish National Research Database-Den Danske Forskningsdatabase

Herbig, Hans-Christian^{6}; Iyengar, Srikanth B.^{5}; Pflaum, Markus J.^{5}

Affiliations:

^{1} Centre for Quantum Geometry of Moduli Spaces, Faculty of Science, Aarhus University, Aarhus University^{2} Department of Mathematical Sciences, Faculty of Science, Aarhus University, Aarhus University^{3} Center for the Topology and Quantization of Moduli Spaces (CTQM), Faculty of Science, Aarhus University, Aarhus University^{4} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University^{5} unknown^{6} Department of Mathematics - Centre for Quantum Geometry of Moduli Spaces, Department of Mathematics, Science and Technology, Aarhus University

DOI:

10.1007/s11005-009-0331-6

Abstract:

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443–461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43–103, 1990) for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

Type:

Journal article

Language:

English

Published in:

Letters in Mathematical Physics, 2009, Vol 89, Issue 2