Weak stuffle algebras


Salle Duhem M3
Cécile Mammez
Vendredi, 29 Mai, 2020 - 14:00 - 15:00
Study the multiple zeta function in algebraic terms leads to the definition of the stuffle product. It is recursively defined by
$x_iu \star x_jv = x_i(u \star x_jv) + x_j(x_iu \star v) + x_{i+j}(u \star v)$
where $x_i,x_j$ are letters and $u, v$ are words. In his thesis, Singer gives the algebraic translation of multiple zeta values with the Schlesinger-Zudilin model (S-Z model) and the Bradley-Zhao model (B-Z model). This leads to the definition of two products where the recursive relation depends on prefix of each words. For instance, we can find letters $y$ and $p$ such as, for any words
$u$ and $v$ :
$yu \lozenge pv = pv \lozenge yu = y(u \lozenge pv).$
In this talk, we give a generalization of the stuffle product, called weak stuffle product, including the case of the S-Z model and the B-Z model. Then we study the structure of the underlying algebra.