Certain group dynamical systems induced by Hecke algebras

• Autorzy: Cho I.

Identyfikatory

DOI

10.7494/OpMath.2016.36.3.337

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study dynamical systems induced by a certain group [formula] embedded in the Hecke algebra H(Gp) induced by the generalized linear group Gp = GL2(Qp) over the p-adic number fields Qp for a fixed prime p. We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms ol free probability on the Hecke algebra H(Gp).

Słowa kluczowe

EN

free probability; free moments; free cumulants; Hecke algebra; normal Hecke subalgebra; free probability spaces; representations; operators; Hilbert spaces; dynamical systems; crossed product algebras

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 3
• Strony: 337--373
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Cho I.

• St. Ambrose University Department of Mathematics and Statistics 421 Ambrose Hall, 518 W. Locust St. Davenport, Iowa, 52803, USA

Bibliografia

• [1] M. Aschbacher, Finite Group Theory, Cambridge Univ. Press, Cambridge, 2000.
• [2] I. Cho, Operators induced by prime numbers, Methods Appl. Math. 19 (2013) 4, 313-340.
• [3] I. Cho, p-adic Banach space operators and adelic Banach space operators, Opuscula Math. 34 (2014) 1, 29-65.
• [4] I. Cho, Representations and corresponding operators induced Hecke algebras, Complex Anal. Oper. Theory, DOI: 10.1007/sll785-014-0418-7, (2014).
• [5] I. Cho, Dynamical systems on arithmetic functions determined by primes, Banach J. Math. Anal. 9 (2015) 1, 173-215.
• [6] I. Cho, Free probability on Hecke algebras and certain group C* -algebras induced by Hecke algebras, Opuscula Math. 36 (2016) 1, 153-187.
• [7] I. Cho, T. Gillespie, Free probability on the Hecke algebra, Compl. Anal. Oper. Theory, DOI: 10.1007/sll785-014-0403-l, (2015).
• [8] I. Cho, P.E.T. Jorgensen, Krein-Space Operators Induced by Dirichlet Characters, Con-temp. Math.: Commutative and Noncommutative Harmonic Analysis and Applications, Amer. Math. Soc. (2014), 3-33.
• [9] I. Cho, P.E.T. Jorgensen, Matrices induced by arithmetic functions, primes, and groupoid actions of directed graphs, Special Matrices (2015), to appear.
• [10] T. Gillespie, Superposition of zeroes of automorphic L-functions and functoriality, Univ. of Iowa, PhD Thesis (2010).
• [11] T. Gillespie, Prime number theorems for Rankin-Selberg L-functions over number fields, Sci. China Math. 54 (2011) 1, 35-46.
• [12] F. Radulescu, Random matrices, amalgamated free products and subfactors of the C*-algebra of a free group of nonsingular index, Invent. Math. 115 (1994), 347-389.
• [13] R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Amer. Math. Soc. Mem. 132 (1998) 627.
• [14] V.S. Vladimirov, LV. Volovich, E.I. Zelenov, p-Adic Analysis and Mathematical Physics, Ser. Soviet & East European Math., vol. 1, World Scientific, 1994.
• [15] D. Voiculescu, K. Dykemma, A. Nica, Free Random Variables, CRM Monograph Series, vol. 1, 1992.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.