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

Ilwoo Cho
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Abstract

064 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, $L(F_{2})*_{L(F_{1})}L(F_{2})=L( )*_{L( )}L( )$ 064 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.

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Ilwoo Cho. 2004-05-21. Moments of the Generating Operator of Two Copies of L(F_2)'s over L(F_1). https://arxiv.org/abs/math/0405107

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