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Deformation quantization for actions of Kahlerian lie groups / Pierre Bieliavsky and Victor Gayral.

By: Contributor(s): Material type: TextTextSeries: Memoirs of the American Mathematical Society ; v 236, no 1115.Publication details: Providence : American Mathematical Society, 2015.Description: v, 154 p. ; 26 cmISBN:
  • 9781470414917 (alk. paper)
Subject(s): DDC classification:
  • 510 23 Am512
Contents:
1. Introduction -- 2. Oscillatory integrals -- 3. Tempered pairs for Kählerian Lie groups -- 4. Non-formal star-products -- 5. Deformation of Fréchet algebras -- 6. Quantization of polarized symplectic symmetric spaces -- 7. Quantization of Kählerian Lie groups -- 8. Deformation of C*-algebras -- Bibliography.
Summary: In this memoir, the authors prove both analogous statements for general negatively curved Kahlerian 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 Calderon-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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Includes bibliographical references.

1. Introduction --
2. Oscillatory integrals --
3. Tempered pairs for Kählerian Lie groups --
4. Non-formal star-products --
5. Deformation of Fréchet algebras --
6. Quantization of polarized symplectic symmetric spaces --
7. Quantization of Kählerian Lie groups --
8. Deformation of C*-algebras --
Bibliography.

In this memoir, the authors prove both analogous statements for general negatively curved Kahlerian 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 Calderon-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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