The Polynomial Endomorphisms of Graph Algebras
Operator Algebras
2018-10-15 v1 Dynamical Systems
Rings and Algebras
Abstract
We investigate polynomial endomorphisms of graph -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.
Keywords
Cite
@article{arxiv.1810.05230,
title = {The Polynomial Endomorphisms of Graph Algebras},
author = {Rune Johansen and Adam P. W. Sørensen and Wojciech Szymański},
journal= {arXiv preprint arXiv:1810.05230},
year = {2018}
}
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29 pages