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
)
∗
L(
F
1
)
L(
F
2
)=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(
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.