Certain group dynamical systems induced by Hecke algebras

Opuscula Mathematica

Ilwoo Cho¹ 

[1] St. Ambrose University, Department of Mathematics and Statistics, 421 Ambrose Hall, 518 W. Locust St., Davenport, Iowa, 52803, USA;

关键词: 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;   

DOI  :  http://dx.doi.org/10.7494/OpMath.2016.36.3.337

来源: DOAJ

【 摘 要 】

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 \(\mathcal{H}(G_{p})\).

【 授权许可】

Unknown