Endomorphisms of graph algebras

Details Endomorphisms of graph algebras Endomorphisms of graph algebras

2011-01-21

arxiv.org/abs/1101.4210v2

Mathematics

Operator Algebras

major revision, 3 figures, uses pictex

Scientific paper

Endomorphisms of graph C*-algebras are investigated. The Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. Criteria of outerness for automorphisms in the restricted Weyl group are found. It is shown that the restriction to the diagonal MASA of an automorphism which globally preserves both the diagonal and the core AF-subalgebra eventually commutes with the shift. Invertibility criteria for localized endomorphisms are given. Proper endomorphisms which restrict to automorphisms of the diagonal MASA are analyzed. A combinatorial approach to analysis of permutative endomorphisms is developed.

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