Deformation quantization for actions of Kählerian Lie groups. Memoirs of the American Mathematical Society; volume 236 (5th of 6 numbers) = number 236.

Bieliavsky, Pierre; Gayral, Victor

ISBN 10: 1470414910 / ISBN 13: 9781470414917

Edité par Providence, American Mathematical Society, 2015

A propos de cet article

Ex-library in GOOD condition with library-signature and stamp(s). Some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-00427 9781470414917 Sprache: Englisch Gewicht in Gramm: 150.

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Détails bibliographiques

• Titre: Deformation quantization for actions of Kählerian Lie groups. Memoirs of the American Mathematical Society; volume 236 (5th of 6 numbers) = number 236.
• Éditeur: Providence, American Mathematical Society
• Date de parution: 2015
• Langue: anglais
• ISBN à 10 chiffres: 1470414910
• ISBN à 13 chiffres: 9781470414917
• Reliure: Softcover
• Poids: 150 grammes
• Catalogues du vendeur:
  • SA MATHEMATIK

A propos de ce titre

Synopsis

Let $\mathbb{B}$ be a Lie group admitting a left-invariant negatively curved Kahlerian structure. Consider a strongly continuous action $\alpha$ of $\mathbb{B}$ on a Frechet algebra $\mathcal{A}$. Denote by $\mathcal{A}^\infty$ the associated Frechet algebra of smooth vectors for this action. In the Abelian case $\mathbb{B}=\mathbb{R}^{2n}$ and $\alpha$ isometric, Marc Rieffel proved that Weyl's operator symbol composition formula (the so called Moyal product) yields a deformation through Frechet algebra structures $\{\star_{\theta}^\alpha\}_{\theta\in\mathbb{R}}$ on $\mathcal{A}^\infty$. When $\mathcal{A}$ is a $C^*$-algebra, every deformed Frechet algebra $(\mathcal{A}^\infty,\star^\alpha_\theta)$ admits a compatible pre-$C^*$-structure, hence yielding a deformation theory at the level of $C^*$-algebras too.

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.

À propos de l'auteur

Pierre Bieliavsky, Universite Catholique de Louvain, Louvain le Neuve, Belgium.

Victor Gayral, Laboratoire de Mathematiques, Reims, France.