Certain group dynamical systems induced by Hecke algebras
In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\) for a fixed prime \(p\)....
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2016-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol36/3/art/opuscula_math_3620.pdf |
| _version_ | 1819231603121979392 |
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| author | Ilwoo Cho |
| author_facet | Ilwoo Cho |
| author_sort | Ilwoo Cho |
| collection | DOAJ |
| description | In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\) for a fixed prime \(p\). We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra \(\mathcal{H}(G_{p})\). |
| first_indexed | 2024-12-23T11:47:35Z |
| format | Article |
| id | doaj.art-a726eac59ba84e998a1e3e7f8e207700 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-23T11:47:35Z |
| publishDate | 2016-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-a726eac59ba84e998a1e3e7f8e2077002022-12-21T17:48:18ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742016-01-01363337373http://dx.doi.org/10.7494/OpMath.2016.36.3.3373620Certain group dynamical systems induced by Hecke algebrasIlwoo Cho0St. Ambrose University, Department of Mathematics and Statistics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USAIn this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\) for a fixed prime \(p\). We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra \(\mathcal{H}(G_{p})\).http://www.opuscula.agh.edu.pl/vol36/3/art/opuscula_math_3620.pdffree probabilityfree probability, free momentsfree cumulantsHecke algebranormal Hecke subalgebrafree probability spacesrepresentationsoperatorsHilbert spacesdynamical systemscrossed product algebras |
| spellingShingle | Ilwoo Cho Certain group dynamical systems induced by Hecke algebras Opuscula Mathematica free probability free probability, free moments free cumulants Hecke algebra normal Hecke subalgebra free probability spaces representations operators Hilbert spaces dynamical systems crossed product algebras |
| title | Certain group dynamical systems induced by Hecke algebras |
| title_full | Certain group dynamical systems induced by Hecke algebras |
| title_fullStr | Certain group dynamical systems induced by Hecke algebras |
| title_full_unstemmed | Certain group dynamical systems induced by Hecke algebras |
| title_short | Certain group dynamical systems induced by Hecke algebras |
| title_sort | certain group dynamical systems induced by hecke algebras |
| topic | free probability free probability, free moments free cumulants Hecke algebra normal Hecke subalgebra free probability spaces representations operators Hilbert spaces dynamical systems crossed product algebras |
| url | http://www.opuscula.agh.edu.pl/vol36/3/art/opuscula_math_3620.pdf |
| work_keys_str_mv | AT ilwoocho certaingroupdynamicalsystemsinducedbyheckealgebras |