Universal solutions for the classical dynamical Yang–Baxter equation and the Maurer–Cartan equations

Abstract

Using functional equations we solve the Maurer–Cartan equations and a special version of the classical dynamical Yang–Baxter equation (vCDYBE). Our solutions are valid for any Lie algebra over a base ring containing , and in the case of vCDYBE for any quadratic Lie algebra. Our method applies also to Lie superalgebras.