Definition and existence of quantum isometry groups
Document Type
Book Chapter
Publication Title
Infosys Science Foundation Series in Mathematical Sciences
Abstract
Under some reasonable assumptions on a spectral triple (A∞, H, D) (which we call admissibility), we prove the existence of a universal object in the category of compact quantum groups admitting coaction on the closure of A∞ which commutes with the (noncommutative) Laplacian. This universal object is called the quantum isometry group w.r.t. the Laplacian. Moreover, we discuss analogous formulations of the quantum group of orientation (and volume or a given real structure) preserving isometries. Sufficient conditions under which the action of the quantum isometry group keeps the C* algebra invariant and is a C* action are given. We also mention some sufficient conditions for the existence of the quantum group of orientation preserving isometries without fixing a choice of the ‘volume-form’.
First Page
69
Last Page
95
DOI
10.1007/978-81-322-3667-2_3
Publication Date
1-1-2016
Recommended Citation
Goswami, Debashish and Bhowmick, Jyotishman, "Definition and existence of quantum isometry groups" (2016). Book Chapters. 227.
https://digitalcommons.isical.ac.in/book-chapters/227
