KMS states and continuous orbit equivalence for ultragraph shift spaces with sinks

• Tasca, Felipe Augusto ^[1] ; Gonçalves, Daniel ^[1]
  1. [1] Universidade Federal de Santa Catarina

     Universidade Federal de Santa Catarina

     Brasil

     
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 66, Nº 2, 2022, págs. 729-787
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • We extend ultragraph shift spaces and the realization of ultragraph C∗-algebras as partial crossed products to include ultragraphs with sinks (under a mild condition, called (RFUM2), which allows us to dismiss the use of filters) and we describe the associated transformation groupoid. Using these characterizations we study continuous orbit equivalence of ultragraph shift spaces (via groupoids) and KMS and ground states (via partial crossed products).

• Referencias bibliográficas
  • F. Abadie, On partial actions and groupoids, Proc. Amer. Math. Soc. 132(4) (2004), 1037–1047. DOI: 10.1090/S0002-9939-03-07300-3
  • S. E. Arklint, S. Eilers, and E. Ruiz, A dynamical characterization of diagonal-preserving *-isomorphisms of graph C∗-algebras, Ergodic Theory...
  • T. Bates, D. Pask, I. Raeburn, and W. Szymanski ´ , The C∗-algebras of rowfinite graphs, New York J. Math. 6 (2000), 307–324.
  • O. Bratteli and D. W. Robinson, “Operator Algebras and Quantum Statistical Mechanics 2. Equilibrium States. Models in Quantum Statistical...
  • N. Brownlowe, T. M. Carlsen, and M. F. Whittaker, Graph algebras and orbit equivalence, Ergodic Theory Dynam. Systems 37(2) (2017), 389–417....
  • T. M. Carlsen and N. S. Larsen, Partial actions and KMS states on relative graph C∗-algebras, J. Funct. Anal. 271(8) (2016), 2090–2132. DOI:...
  • T. M. Carlsen and J. Rout, Diagonal-preserving gauge-invariant isomorphisms of graph C∗-algebras, J. Funct. Anal. 273(9) (2017), 2981–2993....
  • T. M. Carlsen, E. Ruiz, A. Sims, and M. Tomforde, Reconstruction of groupoids and C∗-rigidity of dynamical systems, Adv. Math. 390 (2021),...
  • T. M. Carlsen and M. L. Winger, Orbit equivalence of graphs and isomorphism of graph groupoids, Math. Scand. 123(2) (2018), 239–248. DOI:...
  • J. Christensen, Symmetries of the KMS simplex, Comm. Math. Phys. 364(1) (2018), 357–383. DOI: 10.1007/s00220-018-3250-5
  • G. G. de Castro and D. Gonc¸alves, KMS and ground states on ultragraph C∗-algebras, Integral Equations Operator Theory 90(6) (2018), Paper...
  • G. G. de Castro, D. Gonc¸alves, and D. W. van Wyk, Topological full groups of ultragraph groupoids as an isomorphism invariant, M¨unster J....
  • G. G. de Castro, and F. de L. Mortari, KMS states for the generalized gauge action on graph algebras, C. R. Math. Acad. Sci. Soc. R. Can....
  • G. G. de Castro and D. W. van Wyk, Labelled space C∗-algebras as partial crossed products and a simplicity characterization, J. Math. Anal....
  • G. Edgar, “Measure, Topology, and Fractal Geometry”, Second edition, Undergraduate Texts in Mathematics, Springer, New York, 2008. DOI: 10.1007/978-0-387-74749-1
  • R. Exel, “Partial Dynamical Systems, Fell Bundles and Applications”, Mathematical Surveys and Monographs 224, American Mathematical Society,...
  • R. Exel and M. Laca, Partial dynamical systems and the KMS condition, Comm. Math. Phys. 232(2) (2003), 223–277. DOI: 10.1007/s00220-002-0713-4
  • D. Fiebig and U.-R. Fiebig, Topological boundaries for countable state Markov shifts, Proc. London Math. Soc. (3) 70(3) (1995), 625–643. DOI:...
  • D. Gonçalves and D. Royer, (M + 1)-step shift spaces that are not conjugate to M-step shift spaces, Bull. Sci. Math. 139(2) (2015), 178–183....
  • D. Gonçalves and D. Royer, Ultragraphs and shift spaces over infinite alphabets, Bull. Sci. Math. 141(1) (2017), 25–45. DOI: 10.1016/j.bulsci.2016.10.002
  • D. Gonc¸alves and D. Royer, Infinite alphabet edge shift spaces via ultragraphs and their C∗-algebras, Int. Math. Res. Not. IMRN 2019(7) (2019),...
  • D. Gonçalves and D. Royer, Simplicity and chain conditions for ultragraph Leavitt path algebras via partial skew group ring theory, J. Aust....
  • D. Gonçalves and M. Sobottka, Continuous shift commuting maps between ultragraph shift maps, Discrete Contin. Dyn. Syst. 39(2) (2019), 1033–1048....
  • D. Gonçalves, M. Sobottka, and C. Starling, Sliding block codes between shift spaces over infinite alphabets, Math. Nachr. 289(17-18) (2016),...
  • D. Gonçalves, M. Sobottka, and C. Starling, Two-sided shift spaces over infinite alphabets, J. Aust. Math. Soc. 103(3) (2017), 357–386. DOI:...
  • D. Gonçalves and B. B. Uggioni, Li-Yorke chaos for ultragraph shift spaces, Discrete Contin. Dyn. Syst. 40(4) (2020), 2347–2365. DOI: 10.3934/dcds.2020117
  • D. Gonçalves and B. B. Uggioni, Ultragraph shift spaces and chaos, Bull. Sci. Math. 158 (2020), 102807, 23 pp. DOI: 10.1016/j.bulsci.2019.102807
  • A. an Huef, M. Laca, I. Raeburn, and A. Sims, KMS states on the C∗-algebras of finite graphs, J. Math. Anal. Appl. 405(2) (2013), 388–399....
  • A. an Huef, M. Laca, I. Raeburn, and A. Sims, KMS states on the C∗-algebras of reducible graphs, Ergodic Theory Dynam. Systems 35(8) (2015),...
  • M. Imanfar, A. Pourabbas, and H. Larki, The Leavitt path algebras of ultragraphs, Kyungpook Math. J. 60(1) (2020), 21–43. DOI: 10.5666/KMJ.2020.60.1.21
  • T. Katsura, P. S. Muhly, A. Sims, and M. Tomforde, Ultragraph C∗-algebras via topological quivers, Studia Math. 187(2) (2008), 137–155. DOI:...
  • A. Kumjian, D. Pask, I. Raeburn, and J. Renault, Graphs, groupoids, and Cuntz–Krieger algebras, J. Funct. Anal. 144(2) (1997), 505–541. DOI:...
  • D. Lind and B. Marcus, “An Introduction to Symbolic Dynamics and Coding”, Cambridge University Press, Cambridge, 1995. DOI: 10.1017/CBO9780511626302
  • A. E. Marrero and P. S. Muhly, Groupoid and inverse semigroup presentations of ultragraph C∗-algebras, Semigroup Forum 77(3) (2008), 399–422.DOI:...
  • P. Nyland and E. Ortega, Topological full groups of ample groupoids with applications to graph algebras, Internat. J. Math. 30(4) (2019),...
  • W. Ott, M. Tomforde, and P. N. Willis, One-sided shift spaces over infinite alphabets, New York Journal of Mathematics, NYJM Monographs 5,...
  • G. K. Pedersen, “C∗-Algebras and their Automorphism Groups”, London Mathematical Society Monographs 14, Academic Press, Inc. [Harcourt Brace...
  • F. A. Tasca, Um estudo do espa¸co dos caminhos de fronteira e da C∗-´algebra associada a um ultragrafo com sinks, Thesis (Ph.D.)-Universidade...
  • M. Tomforde, A unified approach to Exel–Laca algebras and C∗-algebras associated to graphs, J. Operator Theory 50(2) (2003), 345–368.
  • M. Tomforde, Simplicity of ultragraph algebras, Indiana Univ. Math. J. 52(4) (2003), 901–925. DOI: 10.1512/iumj.2003.52.2209
  • S. B. G. Webster, The path space of a directed graph, Proc. Amer. Math. Soc. 142(1) (2014), 213–225. DOI: 10.1090/S0002-9939-2013-11755-7