Deformation Quantization for Actions of Kahlerian Lie Groups is popular PDF and ePub book, written by Pierre Bieliavsky in 2015-06-26, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Deformation Quantization for Actions of Kahlerian Lie Groups can be Read Online from any device for your convenience.
Deformation Quantization for Actions of Kahlerian Lie Groups Book PDF Summary
Let B be a Lie group admitting a left-invariant negatively curved Kählerian structure. Consider a strongly continuous action of B on a Fréchet algebra . Denote by the associated Fréchet algebra of smooth vectors for this action. In the Abelian case BR and isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Fréchet algebra structures R on . When is a -algebra, every deformed Fréchet algebra admits a compatible pre- -structure, hence yielding a deformation theory at the level of -algebras too. In this memoir, the authors prove both analogous statements for general negatively curved Kählerian groups. The construction relies on the one hand on combining a non-Abelian version of oscillatory integral on tempered Lie groups with geom,etrical objects coming from invariant WKB-quantization of solvable symplectic symmetric spaces, and, on the second hand, in establishing a non-Abelian version of the Calderón-Vaillancourt Theorem. In particular, the authors give an oscillating kernel formula for WKB-star products on symplectic symmetric spaces that fiber over an exponential Lie group.
Detail Book of Deformation Quantization for Actions of Kahlerian Lie Groups PDF
- Author : Pierre Bieliavsky
- Release : 26 June 2015
- Publisher : American Mathematical Soc.
- ISBN : 9781470414917
- Genre : Mathematics
- Total Page : 166 pages
- Language : English
- PDF File Size : 12,6 Mb
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