On Hilbert evolution algebras of a graph
Abstract
Evolution algebras are a special class of non-associative algebras exhibiting connections with different fields of Mathematics. Hilbert evolution algebras generalize the concept through a framework of Hilbert spaces. This allows to deal with a wide class of infinite-dimensional spaces. In this work we study Hilbert evolution algebras associated to a graph. Inspired in definitions of evolution algebras we define the Hilbert evolution algebra associated to a given graph and the Hilbert evolution algebra associated to the symmetric random walk on a graph. For a given graph, we provide conditions under which these structures are or are not isomorphic. Our definitions and results extend to graphs with infinitely many vertices a similar theory developed for evolution algebras associated to finite graphs.
Cite
@article{arxiv.2111.07399,
title = {On Hilbert evolution algebras of a graph},
author = {Sebastian J. Vidal and Paula Cadavid and Pablo M. Rodriguez},
journal= {arXiv preprint arXiv:2111.07399},
year = {2021}
}