Stuffle regularized multiple Eisenstein series revisited

Multiple Eisenstein series are holomorphic functions in the complex upper-half plane, which can be seen as a crossbreed between multiple zeta values and classical Eisenstein series. They were originally defined by Gangl-Kaneko-Zagier in 2006, and since then, many variants and regularizations of them have been studied. They give a natural bridge between the world of modular forms and multiple zeta values. In this note, we give a new algebraic interpretation of stuffle regularized multiple Eisenstein series based on the Hopf algebra structure of the harmonic algebra introduced by Hoffman.