This talk was part of the Mini-course on "Courant algebroids, generalized Ricci flow, and T-duality" held September 7 - 11, 2020 at the ESI.
We present a new class of classical integrable models that originates from deformations of associative algebras.
We show that each deformation of an associaitive algebra can be used to construct a certain strong homotopy algebra that equipes us with a nilpotent differential in the target space and the integrable model can be written as the AKSZ-model. Integrability is demonstrated via a Lax pair and by explicitly constructing the general solution of the equations.
A large class of such deformations originates from the deformation quantization of Poisson manifolds equipped with discrete symmetries - Poisson Orbifolds. The relation of this construction to Higher Spin Gravities and to dualities in Chern-Simons matter theories is briefly discussed.
