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  • P-ISSN3059-0604
  • E-ISSN3059-1309
  • KCI

ISSN : 3059-0604

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Vol.19 No.2

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DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS

DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: Theoretical Mathematics and Pedagogical Mathematics, (P)3059-0604; (E)3059-1309
2012, v.19 no.2, pp.199-209
https://doi.org/10.7468/jksmeb.2012.19.2.199
Yi, In-Hyeop (Department of Mathematics Education, Ewha Womans University)
Yi, In-Hyeop. (2012). DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS, 19(2), 199-209, https://doi.org/10.7468/jksmeb.2012.19.2.199

Abstract

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

keywords
higher rank graphs, path groupoid, groupoid algebra

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한국수학교육학회지시리즈B:순수및응용수학

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