Free probability on Hecke algebras and certain group C*-algebras induced by Hecke algebras

• Autorzy: Cho I.

Identyfikatory

DOI

http://dx.doi.Org/10.7494/OpMath.2016.36.2.153

• Języki publikacji: EN

Abstrakty

EN

In this paper, by establishing free-probabilistic models on the Hecke algebras [formula] induced by p-adic number fields Qp, we construct free probability spaces for all primes p. Hilbert-space representations are induced by such free-probabilistic structures. We study C*-algebras induced by certain partial isometries realized under the representations.

Słowa kluczowe

EN

free probability; free moments; free cumulants; Hecke algebras; normal Hecke subalgebras; representations; groups; group C*-algebras

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2016
• Tom: Vol. 36, no. 2
• Strony: 153--187
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Cho I.

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

Bibliografia

• [1] I. Cho, Operators induced by prime numbers, Methods Appl. Math. 19 (2013) 4, 313-340.
• [2] I. Cho, Representations and corresponding operators induced by Hecke algebras, Complex. Anal. Oper. Theory, DOI: 10.1007/sll785-014-0418-7, (2014).
• [3] I. Cho, p-adic Banach space operators and adelic Banach space operators, Opuseula Math. 34 (2014) 1, 29-65.
• [4] I. Cho, Free distributional data of arithmetic functions and corresponding generating functions, Complex. Anal. Oper. Theory 8 (2014) 2, 537-570.
• [5] I. Cho, Dynamical systems of arithmetic functions determined by primes, Banach J. Math. Anal. 9 (2015), 173-215.
• [6] I. Cho, Classification on arithmetic functions and corresponding free-moment L-functions, Bulletin Korean Math. Soc. (2015), to appear.
• [7] I. Cho, T. Gillespie, Free probability on the Hecke algebra, Complex Anal. Oper. Theory, DOI: 10.1007/sll785-014-0403-l, (2014).
• [8] I. Cho, P.E.T. Jorgensen, Krein-space representations of arithmetic functions dertermined by primes, Alg. Rep. Theo. 17 (2014) 6, 1809-1841.
• [9] T. Gillespie, Superposition of zeroes of automorphic L-functions and functoriality, PhD Thesis, Univ. ol Iowa, (2010).
• [10] T. Gillespie, Prime number theorems for Rankin-Selberg L-functions over number fields, Sci. China Math. 54 (2011) 1, 35-46.
• [11] 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.
• [12] R. Speicher, Combinatorial theory of the free product with amalgamation and operator-valued free probability theory, Amer. Math. Soc. Mem. 132 (1998) 627.
• [13] D. Voiculescu, K. Dykemma, A. Nica, Free Random Variables, vol. 1, CRM Monograph Series, 1992.
• [14] V.S. Vladimirov, LV. Volovich, E.I. Zelenov, p-Adic Analysis and Mathematical Physics, vol. 1, Ser. Soviet & East European Math., World Scientific, 1994.

Uwagi

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