DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS

Yi, In-Hyeop; Yi, In-Hyeop

doi:10.7468/jksmeb.2012.19.2.199

P-ISSN1226-0657
E-ISSN2287-6081
KCI

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Vol.19 No.2

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DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2012, v.19 no.2, pp.199-209

https://doi.org/10.7468/jksmeb.2012.19.2.199

Yi, In-Hyeop

Yi,, I. (2012). DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(2), 199-209, https://doi.org/10.7468/jksmeb.2012.19.2.199

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Abstract

For a locally compact higher rank graph <TEX>${\Lambda}$</TEX>, we construct a two-sided path space <TEX>${\Lambda}^{\Delta}$</TEX> with shift homeomorphism <TEX>${\sigma}$</TEX> and its corresponding path groupoid <TEX>${\Gamma}$</TEX>. Then we find equivalent conditions of aperiodicity, cofinality and irreducibility of <TEX>${\Lambda}$</TEX> in (<TEX>${\Lambda}^{\Delta}$</TEX>, <TEX>${\sigma}$</TEX>), <TEX>${\Gamma}$</TEX>, and the groupoid algebra <TEX>$C^*({\Gamma})$</TEX>.

keywords: higher rank graphs, path groupoid, groupoid algebra

Reference

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Article Contents

Vol.19 No.2

DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS

Abstract

Reference

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics