The polynomial endomorphisms of graph algebras

Rune Johansen, Adam P. W. Sørensen, Wojciech Szymanski

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Abstrakt

We investigate polynomial endomorphisms of graph C -algebras and Leavitt path algebras. To this end, we define and analyze the coding graph corresponding to each such an endomorphism. We find an if and only if condition for the endomorphism to restrict to an automorphism of the diagonal MASA, which is stated in terms of synchronization of a certain labelling on the coding graph. We show that the dynamics induced this way on the space of infinite paths (the spectrum of the MASA) is generated by an asynchronous transducer.

OriginalsprogEngelsk
TidsskriftGroups, Geometry, and Dynamics
Vol/bind14
Udgave nummer3
Sider (fra-til)1043-1075
ISSN1661-7207
DOI
StatusUdgivet - 27. okt. 2020

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