The polynomial endomorphisms of graph algebras

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

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Abstract

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.

Original languageEnglish
JournalGroups, Geometry, and Dynamics
Volume14
Issue number3
Pages (from-to)1043-1075
ISSN1661-7207
DOIs
Publication statusPublished - 27. Oct 2020

Keywords

  • automorphism
  • endomorphism
  • graph algebra
  • Leavitt path algebra
  • MASA
  • Automorphism
  • Endomorphism
  • Graph algebra

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