Moments of the Generating Operator of Two Copies of L(F_2)'s over L(F_1)

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, $L(F_2){\ast }_{L(F_1)}L(F_2)=L(<a,b>){\ast }_{L(<h>)}L(<c,d>)$ 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 $L(F_1)$ is used and some combinatorial functions (to explain the recurrence relations) are used to figure out the $n$-th moment of this element.

63 pages, It is presented in COSy 2004