1999/05/27 by Nikolai Neumaier, Neumaier, Nikolai
Mathematics · Physics and Astronomy · #81S10 (Primary) 81R99 (Secondary) #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.QA #math.SG #msc:81R99 #msc:81S10
paper · pdf · doi:10.48550/arxiv.math/9905176
LaTeX2e, 18 pages, title changed, one definition and one proposition added to section 5
openalex publication_date 1999/05/27 · arxiv created 1999/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we explicitly construct local ν-Euler derivations \mathsf Eα= ν∂ν+ \Lieξα + \mathsf Dα, where the ξα are local, conformally symplectic vector fields and the \mathsf Dα are formal series of locally defined differential operators, for Fedosov star products on a symplectic manifold (M,ω) by means of which we are able to compute Deligne's characteristic class of these star products. We show that this class is given by 1/ν[ω]+1/ν[Ω] where Ω= ∑i=1^∞ νi Ωi is a formal series of closed two-forms on M the cohomology class of which coincides with the one introduced by Fedosov to classify his star products. Moreover, our result implies that the normalisation condition used by Fedosov does not have any effect on the isomorphy class of the resulting star product. Finally we consider star products that have additional algebraic structures and compute the effect of these structures on the corresponding characteristic classes of these star products. Specifying the constituents of Fedosov's construction we obtain star products with these special properties. Finally we investigate equivalence transformations between such special star products and prove existence of equivalence transformations being compatible with the considered algebraic structures.