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K ‐theory of the Boutet de Monvel algebra with classical SG‐symbols on the half space
Author(s) -
Lopes Pedro T. P.,
Melo Severino T.
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201300357
Subject(s) - mathematics , homomorphism , algebra over a field , kernel (algebra) , algebra homomorphism , bounded function , order (exchange) , extension (predicate logic) , pure mathematics , discrete mathematics , mathematical analysis , finance , computer science , economics , programming language
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 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 ofR + n × R nandR n − 1 × 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.