Reference : Formal connections for families of star products

	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/22573

Title :	Formal connections for families of star products
Language :	English
Author, co-author :	Andersen, Joergen [Aarhus Universitet - AU > Department of Mathematics > > Professor]
	Masulli, Paolo [University of Lausanne (Lausanne, Switzerland) > Faculty of Business and Economics (HEC) and Faculty of Law, Criminal Justice and Public Administration (FDCA) > > postdoc]
	Schatz, Florian [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	2016
Journal title :	Communications in Mathematical Physics
Publisher :	Springer Science & Business Media B.V.
Volume :	342
Issue/season :	2
Pages :	739-768
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0010-3616
e-ISSN :	1432-0916
Keywords :	[en] deformation quantization ; Hitchin connection ; star products
Abstract :	[en] We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection defined in. We establish a necessary and sufficient condition that guarantees the existence of a formal connection, and we describe the space of formal connections for a family as an affine space modelled by the derivations of the star products. Moreover we show that if the parameter space has trivial first cohomology group any two flat formal connections are related by an automorphism of the family of star products.
Research centres :	Center of Quantum Geometry of Moduli Spaces, Aarhus University (Aarhus, Denmark)
Funders :	Danish National Research Foundation by the Center of excellence grant ’Centre for Quantum Geometry of Moduli Spaces’ (DNRF 95
Target :	Researchers
Permalink :	http://hdl.handle.net/10993/22573
DOI :	10.1007/s00220-016-2574-2
Other URL :	http://link.springer.com/article/10.1007/s00220-016-2574-2
Mentions required by the publisher for OA :	The article appeared online originally at http://link.springer.com/article/10.1007/s00220-016-2574-2

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