Moments of the Generating Operator of Two Copies of L(F₂)'s over L(F₁)

2004/05/06 by Ilwoo Cho, Cho, Ilwoo
Mathematics · #47-xx #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:47-xx

paper · pdf · doi:10.48550/arxiv.math/0405107

63 pages, It is presented in COSy 2004

arxiv created 2004/05/21 · arxiv updated 2009/12/01

Abstract

064<p type="texpara" tag="Body Text" et="abstract" bin="clone" >In this paper, we will consider an example of a (scalar-valued) moment series, under the compatibility. Suppose that we have an amalgamated free product of free group algebras, L(F₂)*_L(F₁)L(F₂)=L(<a,b>)*_L(<h>)L(<c,d>) 064<p type="texpara" tag="Body Text" et="abstract" bin="clone" >We will provide the method how to find the moment series of a+b+a^-1+b^-1+c+d+c^-1+d^-1. Amalgamated freeness of a+b+a^-1+b^-1 and c+d+c^-1+d^-1 over L(F₁) is used and some combinatorial functions (to explain the recurrence relations) are used to figure out the n-th moment of this element.

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