On strong affine representations of the polycyclic monoids

Miklos Hartmann; Tamas Waldhauser

On strong affine representations of the polycyclic monoids

Mathematics

Research output: Working paper

Abstract

Jones and the second author have discovered in [4] that certain representations of the so-called polycyclic monoids are closely related to the representations of the Cuntz algebras Cn studied by Bratteli and Jorgenssen in [2]. We investigate these representations of the polycyclic monoids, generalise some results from [4], give a (sharp) upper bound on the number of atoms in case one of the parameters tends to infinity and present an infinite family of representations having only one atom. Furthermore, by making use of a C++ program we present some observations regarding the ratio of atoms to the number of possible atoms in the n = 3 case.

Original language	English
Pages	1-16
Number of pages	16
Publication status	Published - 2014

Access to Document

http://www.math.u-szeged.hu/~hartm/PDFs/polyart3.pdf

Cite this

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title = "On strong affine representations of the polycyclic monoids",

abstract = "Jones and the second author have discovered in [4] that certain representations of the so-called polycyclic monoids are closely related to the representations of the Cuntz algebras Cn studied by Bratteli and Jorgenssen in [2]. We investigate these representations of the polycyclic monoids, generalise some results from [4], give a (sharp) upper bound on the number of atoms in case one of the parameters tends to infinity and present an infinite family of representations having only one atom. Furthermore, by making use of a C++ program we present some observations regarding the ratio of atoms to the number of possible atoms in the n = 3 case.",

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AU - Waldhauser, Tamas

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N2 - Jones and the second author have discovered in [4] that certain representations of the so-called polycyclic monoids are closely related to the representations of the Cuntz algebras Cn studied by Bratteli and Jorgenssen in [2]. We investigate these representations of the polycyclic monoids, generalise some results from [4], give a (sharp) upper bound on the number of atoms in case one of the parameters tends to infinity and present an infinite family of representations having only one atom. Furthermore, by making use of a C++ program we present some observations regarding the ratio of atoms to the number of possible atoms in the n = 3 case.

AB - Jones and the second author have discovered in [4] that certain representations of the so-called polycyclic monoids are closely related to the representations of the Cuntz algebras Cn studied by Bratteli and Jorgenssen in [2]. We investigate these representations of the polycyclic monoids, generalise some results from [4], give a (sharp) upper bound on the number of atoms in case one of the parameters tends to infinity and present an infinite family of representations having only one atom. Furthermore, by making use of a C++ program we present some observations regarding the ratio of atoms to the number of possible atoms in the n = 3 case.

M3 - Working paper

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BT - On strong affine representations of the polycyclic monoids

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