Abstract
Let 𝔄 be a commutative ℚ-algebra, A be an alphabet of non-commutative letters and 𝔥1 be the non-commutative polynomial algebra generated by the set A over the algebra 𝔄. The harmonic algebra 𝔥1 is closely related to multiple zeta values and multiple zeta-star values in some special case. Some identities in the algebra 𝔥1 are given.
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