Phase transition on the Toeplitz algebra of the affine semigroup over the natural numbers
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Publication:990745
DOI10.1016/j.aim.2010.03.007zbMath1203.46045arXiv0907.3760OpenAlexW2016739913MaRDI QIDQ990745
Publication date: 1 September 2010
Published in: Advances in Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0907.3760
phase transitionKMS statesToeplitz algebraboundary quotientNica covariancequasi-lattice ordered group
Noncommutative dynamical systems (46L55) Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.) (47L80)
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Cites Work
- Boundary quotients and ideals of Toeplitz \(C^{*}\)-algebras of Artin groups
- On \(O_ n\).
- Extension of spontaneous symmetry breaking of Bost-Connes in case of arbitrary global fields
- Semigroups of *-endomorphisms, Dirichlet series, and phase transitions
- Partial dynamical systems and the KMS condition
- KMS states of quasi-free dynamics on Pimsner algebras
- Hecke algebras, type III factors and phase transitions with spontaneous symmetry breaking in number theory
- Semigroup crossed products and the Toeplitz algebras of nonabelian groups
- Phase transition in the Connes-Marcolli \(\mathrm{GL}_2\)-system
- On the Toeplitz algebras of right-angled and finite-type Artin groups
- A Semigroup Crossed Product Arising in Number Theory
- Partial dynamical systems and C*-algebras generated by partial isometries
- Ergodicity of the action of the positive rationals on the group of finite adeles and the Bost-Connes phase transition theorem
- Phase transitions on Hecke C*-algebras and class-field theory over ℚ
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