{"product_id":"9781470414917","title":"Deformation Quantization for Actions of Kahlerian Lie Groups","description":"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.","brand":"Pierre Bieliavsky","offers":[{"title":"Default Title","offer_id":46776499601726,"sku":"9781470414917","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470414917_1609d1ef-484f-4e28-a39f-208db194fc71.jpg?v=1707476974","url":"https:\/\/exclusivebooks.co.za\/products\/9781470414917","provider":"Exclusive Books Online","version":"1.0","type":"link"}