(K\)-Theory of Boutet de Monvel algebras with classical SG-symbols on the half space

We compute the \(K\)-groups of the \(C^{*}\)-algebra of bounded operators generated by the Boutet de Monvel operators with classical SG-symbols of order (0,0) and type 0 on \(\mathbb{R}_{+}^{n}\), as defined by Schrohe, Kapanadze and Schulze. In order to adapt the techniques used in Melo, Nest, Schi...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2013-12
Main Authors: Lopes, Pedro T P, Melo, Severino T
Format: Article
Language:English
Subjects:
Algebra
Group theory
Homomorphisms
Operators (mathematics)
Symbols
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We compute the \(K\)-groups of the \(C^{*}\)-algebra of bounded operators generated by the Boutet de Monvel operators with classical SG-symbols of order (0,0) and type 0 on \(\mathbb{R}_{+}^{n}\), as defined by Schrohe, Kapanadze and Schulze. In order to adapt the techniques used in Melo, Nest, Schick and Schrohe's work on the K-theory of Boutet de Monvel's algebra on compact manifolds, we regard the symbols as functions defined on the radial compactifications of \(\mathbb{R}_{+}^{n}\times\mathbb{R}^{n}\) and \(\mathbb{R}^{n-1}\times\mathbb{R}^{n-1}\). This allows us to give useful descriptions of the kernel and the image of the continuous extension of the boundary principal symbol map, which defines a \(C^{*}\)-algebra homomorphism. We are then able to compute the \(K\)-groups of the algebra using the standard K-theory six-term cyclic exact sequence associated to that homomorphism.
ISSN:2331-8422