Polyvector deformations in eleven-dimensional supergravity

We consider 3- and 6-vector deformations of 11-dimensional supergravity backgrounds of the form M5×M6 admitting at least three Killing vectors. Using flux formulation of the E6(6) exceptional field theory, we derive (sufficient) conditions for the deformations to generate a solution. In the group manifold case, these generalizations of the classical Yang-Baxter equation for the case of r-matrices with three and six indices are shown to reproduce those obtained from exceptional Drinfeld algebra for E6(6). In general, we see an additional constraint, which might be related to higher exceptional Drinfeld algebras