Description
We show that the most general cubic action for a set of even and odd forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H is given by a natural generalization of the Frobenius-Chern-Simons (FCS) model proposed in arXiv:505.04957 as a minimal bosonic 4D higher spin gravity theory. The result is a cubic FCS action for a superconnection valued in H X F where F is a Z2-graded quasi-Frobenius algebra. Unital element not necessary of the general model is subsequently introduced. An example of such a model is given based on Clifford algebra C_2n and it is shown to provide a nontrivial FCS extension of the bosonic Konstein--Vasiliev model with gauge algebra hu (2^(n-1),0).
