Lucio Centrone "Embedding theorems as a bridge between supertraces and supergeometry"

Any algebra herein is intended over a field of characteristic 0. Let E denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional central simple algebra A and a supertrace algebra B, so that B belongs to the same variety of A⊗ E, we study conditions on B so that it can be embedded into A⊗ Ξ, where Ξ is a supercommutative algebra, called A-universal supermap of B, provided B satisfies all the supertrace identities of A⊗E. We use this result in order to relate the formal smoothness of B with that of its A-universal supermap.

Actually, this work acts in the environment of superrepresentations of algebras.