The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS

  • Yi, In-Hyeop (Department of Mathematics Education, Ewha Womans University)
  • Received : 2012.05.10
  • Accepted : 2012.05.23
  • Published : 2012.05.31
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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 $C^*({\Gamma})$.

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References

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