2014/09/11 by Victor Gayral, Gayral, Victor, David Jondreville +1
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #Operator Algebras (math.OA) #math.FA #math.NT #math.OA
paper · pdf · doi:10.48550/arxiv.1409.3349
openalex publication_date 2014/09/11 · arxiv created 2015/01/20 · arxiv updated 2015/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main objective of this article is to develop the theory of deformation of C^*-algebras endowed with a group action, from the perspective of non-formal equivariant quantization. This program, initiated in \citeBieliavsky-Gayral, aims to extend Rieffel's deformation theory \citeRi for more general groups than \mathbb Rd. In \citeBieliavsky-Gayral, we have constructed such a theory for a class of non-Abelian Lie groups. In the present article, we study the somehow opposite situation of Abelian but non-Lie groups. More specifically, we construct here a deformation theory of C^*-algebras endowed with an action of a finite dimensional vector space over a non-Archimedean local field of characteristic different from 2. At the root of our construction stands the p-adic version of the Weyl quantization introduced by Haran and further extended by Bechata and Unterberger.