Deformation quantization for actions of Kählerian Lie groups

著者

• Bieliavsky, Pierre
• Gayral, Victor

書誌事項

Deformation quantization for actions of Kählerian Lie groups

Pierre Bieliavsky, Victor Gayral

（Memoirs of the American Mathematical Society, no. 1115）

American Mathematical Society, 2015, c2014

注記

"Volume 236, number 1115 (fifth of 6 numbers), July 2015"

Includes bibliographical references (p. 153-154)

内容説明・目次

内容説明

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.

目次

Introduction Notations and conventions Oscillatory integrals Tempered pairs for Kahlerian Lie groups Non-formal star-products Deformation of Frechet algebras Quantization of polarized symplectic symmetric spaces Quantization of Kahlerian Lie groups Deformation of $C^*$-algebras Bibliography

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詳細情報

• NII書誌ID(NCID): BB19166145
• ISBN:
  • 9781470414917
• LCCN: 2015007760
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.
• ページ数/冊数: v, 154 p.
• 大きさ: 26 cm
• 親書誌ID:
  • BA00035927