The motivic Galois group for a double zeta value

Paper

Abstract

We consider multiple zeta values, which are periods of mixed Tate motives over

. For a given multiple zeta value

, there exists a unique minimal motive

such that

is a period of

. In general, the motive

is difficult to compute. In this article, we compute the minimal motive

associated to a given double zeta value

. We also compute the motivic Galois group

associated to

and discuss its dimension. Moreover, we give a period matrix of

. The period conjecture predicts that the dimension of

equals the transcendence degree of the algebra of periods of

. Hence our results lead to conjectures about algebraic relations between single and double zeta values.