Fr\'echet algebraic deformation quantization of the Poincar\'e disk

Autor:	Beiser, Svea, Waldmann, Stefan
Rok vydání:	2011
Předmět:	Mathematics - Quantum Algebra Mathematical Physics Mathematics - Functional Analysis 53D55 53D20 46K05 46K10 46H05 81S10 81R60
Druh dokumentu:	Working Paper
Popis:	Starting from formal deformation quantization we use an explicit formula for a star product on the Poincar\'e disk D_n to introduce a Fr\'echet topology making the star product continuous. To this end a general construction of locally convex topologies on algebras with countable vector space basis is introduced and applied. Several examples of independent interest are investigated as e.g. group algebras over finitely generated groups and infinite matrices. In the case of the star product on D_n the resulting Fr\'echet algebra is shown to have many nice features: it is a strongly nuclear K\"othe space, the symmetry group SU(1, n) acts smoothly by continuous automorphisms with an inner infinitesimal action, and evaluation functionals at all points of D_n are continuous positive functionals. Comment: 57 pages, minor update
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1108.2004 Zobrazit plný text záznamu View this record from Arxiv