$t$-adic symmetrization map on harmonic algebra

Abstract: Bachmann, Takeyama and Tasaka introduced a

m a t h b b Q

-linear map

p h i

, which we call the symmetrization map in this paper, on the harmonic algebra

m a t h f r a k H^{1}

. They calculated

p h i (w)

explicitly for an element

w

in

m a t h f r a k H^{1}

related to the multiple zeta values of Mordell--Tornheim type. In this paper, we introduce its

t

-adic generalization

w i d e h a t p h i

and calculate

w i d e h a t p h i (w)

for an element

w

in

m a t h f r a k H^{1} [[t]]

constructed from the theory of

2

-colored rooted tree.

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