Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function
In this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields ℚp (for primes p), and free pro...
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| Format: | Article |
| Language: | English |
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MDPI AG
2015-12-01
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| Series: | Mathematics |
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| Online Access: | http://www.mdpi.com/2227-7390/3/4/1095 |
| _version_ | 1819062696561082368 |
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| author | Ilwoo Cho Palle E. T. Jorgensen |
| author_facet | Ilwoo Cho Palle E. T. Jorgensen |
| author_sort | Ilwoo Cho |
| collection | DOAJ |
| description | In this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields ℚp (for primes p), and free probability on the subalgebra Φ, generated by the Euler totient function ϕ, of the arithmetic algebra A , consisting of all arithmetic functions. In particular, we apply such free probability to consider operator-theoretic and operator-algebraic properties of W * -dynamical systems induced by ℚp under free-probabilistic (and hence, spectral-theoretic) techniques. |
| first_indexed | 2024-12-21T15:02:53Z |
| format | Article |
| id | doaj.art-c5ee477cecee46239e9b746b84dfa273 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-21T15:02:53Z |
| publishDate | 2015-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c5ee477cecee46239e9b746b84dfa2732022-12-21T18:59:33ZengMDPI AGMathematics2227-73902015-12-01341095113810.3390/math3041095math3041095Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient FunctionIlwoo Cho0Palle E. T. Jorgensen1Department of Mathematics, St. Ambrose University, 421 Ambrose Hall, 518 W. Locust St., Davenport, IA 52803, USADepartment of Mathematics, University of Iowa, 14 McLean Hall, Iowa City, IA 52242, USAIn this paper, we study relations between free probability on crossed product W * -algebras with a von Neumann algebra over p-adic number fields ℚp (for primes p), and free probability on the subalgebra Φ, generated by the Euler totient function ϕ, of the arithmetic algebra A , consisting of all arithmetic functions. In particular, we apply such free probability to consider operator-theoretic and operator-algebraic properties of W * -dynamical systems induced by ℚp under free-probabilistic (and hence, spectral-theoretic) techniques.http://www.mdpi.com/2227-7390/3/4/1095p-Adic number fields ℚpp-Adic von neumann algebras ℳp dynamical systems induced by ℚp arithmetic functions the arithmetic algebra A the euler totient function ϕ |
| spellingShingle | Ilwoo Cho Palle E. T. Jorgensen Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function Mathematics p-Adic number fields ℚp p-Adic von neumann algebras ℳp dynamical systems induced by ℚp arithmetic functions the arithmetic algebra A the euler totient function ϕ |
| title | Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function |
| title_full | Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function |
| title_fullStr | Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function |
| title_full_unstemmed | Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function |
| title_short | Free W*-Dynamical Systems From p-Adic Number Fields and the Euler Totient Function |
| title_sort | free w dynamical systems from p adic number fields and the euler totient function |
| topic | p-Adic number fields ℚp p-Adic von neumann algebras ℳp dynamical systems induced by ℚp arithmetic functions the arithmetic algebra A the euler totient function ϕ |
| url | http://www.mdpi.com/2227-7390/3/4/1095 |
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