Abstract
We initiate a systematic investigation of endomorphisms of graph C⁎-algebras C⁎(E), extending several known results on endomorphisms of the Cuntz algebras On. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA DE of C⁎(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C⁎-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show that the restriction to the diagonal MASA of an automorphism which globally preserves both DE and the core AF-subalgebra eventually commutes with the corresponding one-sided shift. Secondly, we exhibit several properties of proper endomorphisms, investigate invertibility of localized endomorphisms both on C⁎(E) and in restriction to DE, and develop a combinatorial approach to analysis of permutative endomorphisms.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
