Graph reconstruction and quantum statistical mechanics

Cornelissen, Gunther; Marcolli, Matilde

doi:10.1016/j.geomphys.2013.03.021

Cited by 10 publications

(17 citation statements)

References 15 publications

(21 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We remark that recently Cornelissen and Marcolli have used the theory of multivariable (automorphic) dynamical systems of Davidson and Katsoulis [12] in the context of number theory (see [6,Theorem 2] and [7,Section 6]) and the reconstruction of graphs (see [8,Theorem 1.5] and the proof of [8, Theorem 1.6]). Proof.…”

Section: Graphs and C * -Dynamical Systemsmentioning

confidence: 99%

“…We remark that semicrossed products and multivariable dynamical systems have been under considerable investigation for the last four decades (for example, [1, 3, 9-12, 16, 19, 28, 30, 33, 35] to mention but a few). Recently, Cornelissen and Marcolli have provided a link that connects the theory of Davidson and Katsoulis [12] for multivariable (automorphic) dynamical systems with number theory [6,7] and reconstruction of graphs [8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Dirichlet property for tensor algebras

Kakariadis

2013

Bulletin of the London Mathematical Society

View full text Add to dashboard Cite

We prove that the tensor algebra of a C * -correspondence X is Dirichlet if and only if X is a Hilbert bimodule. As a consequence, we point out and fix an error appearing in the proof of a famous result of Duncan. Secondly, we answer a question raised by Davidson and Katsoulis concerning tensor algebras and semi-Dirichlet algebras, by giving an example of a Dirichlet algebra that cannot be described as the tensor algebra of any C * -correspondence. Furthermore, we show that the adding tail technique, as extended by the author and Katsoulis, applies in a unique way to preserve the class of Hilbert bimodules.The exploitation of these ideas implies that the tensor algebra of row-finite graphs, the tensor algebra of multivariable automorphic C * -dynamics and Peters' semicrossed product of an injective C * -dynamical system have the unique extension property. The two latter provide examples of non-separable operator algebras that admit a Choquet boundary in the sense of Arveson.

show abstract

Section: Graphs and C * -Dynamical Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Dirichlet property for tensor algebras

Kakariadis

2013

Bulletin of the London Mathematical Society

View full text Add to dashboard Cite

show abstract

“…Such constructions have found applications to other fields of mathematics. In particular, ideas and results by the first author and Katsoulis [32] are used in number theory and graph theory by Cornelissen [24] and Cornelissen-Marcolli [25,26], leaving open the possibility for future interaction.…”

Section: Introductionmentioning

confidence: 99%

Semicrossed products of operator algebras by semigroups

2017

View full text Add to dashboard Cite

show abstract

“…Our motivation relies on the interaction of that theory with other fields of mathematics. In a series of papers Cornelissen [7] and Cornelissen and Marcolli [8,9] illustrate such a strong link by inserting and applying the seminal work on piecewise conjugacy of Davidson and Katsoulis [12] into number theory and the reconstruction of graphs. It remains an open problem whether piecewise conjugacy implies unitary equivalence for multivariable classical systems, and thus whether these two notions coincide.…”

Section: Introductionmentioning

confidence: 99%