2007/09/07 by Pierre Bieliavsky, Bieliavsky, Pierre · 1 citation
Mathematics · Physics and Astronomy · #53D50 #58B34 #81S10 #81V25 #83C57 #Advanced Topics in Algebra #Black Holes and Theoretical Physics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0709.1110
openalex publication_date 2007/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define a universal deformation formula (UDF) for the actions of the affine group on Frechet algebras. More precisely, starting with any associative Frechet algebra which the affine group acts on in a strongly continuous and isometrical manner, the UDF produces a family of topological associative algebra structures on the space of smooth vectors of the action deforming the initial product. The deformation field obtained is based over an infinite dimensional parameter space naturally associated with the space of pseudo-differential operators on the real line. This note also presents some geometrical aspects of the UDF and in particular its relation with hyperbolic geometry.