Symmetry for algebras associated to Fell bundles over groups and groupoids

Autor:	Flores, Felipe, Jauré, Diego, Mantoiu, Marius
Rok vydání:	2021
Předmět:	Mathematics - Operator Algebras Mathematics - Functional Analysis Primary 43A20 20L05 Secondary 47L65 47L30
Druh dokumentu:	Working Paper
Popis:	To every Fell bundle $\mathscr C$ over a locally compact group ${\sf G}$ one associates a Banach $^*$-algebra $L^1({\sf G}\,\vert\,\mathscr C)$. We prove that it is symmetric whenever ${\sf G}$ with the discrete topology is rigidly symmetric. This generalizes the known case of a global action without a twist. There is also a weighted version as well as a treatment of some classes of associated integral kernels. We also deal with the case of Fell bundles over discrete groupoids. We formulate a generalization of rigid symmetry in this case and show its equivalence with an a priori stronger concept. We also study the symmetry of transformation groupoids and some permanence properties. Comment: 26 pages. Major changes with respect to the previous version. To appear in J. Operator Theory
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2110.10814 Zobrazit plný text záznamu View this record from Arxiv