Deformation Quantization for Actions of Kahlerian Lie Groups

Released on by Pierre Bieliavsky
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  • Deformation Quantization for Actions of Kahlerian Lie Groups Book Detail

  • Author : Pierre Bieliavsky
  • Release Date : 2015-06-26
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 166
  • ISBN 13 : 1470414910
  • File Size : 75,75 MB
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Deformation Quantization for Actions of Kahlerian Lie Groups by Pierre Bieliavsky PDF Summary

Book Description: 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.

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New Trends in Noncommutative Algebra

New Trends in Noncommutative Algebra

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This volume contains the proceedings of the conference `New Trends in Noncommutative Algebra', held at the University of Washington, Seattle, in August 2010. Th