Non-self-similarity conjecture for the associative superalgebra generated by pivot elements

Let $A=\operatorname{Alg}(v_0,v_1)$ be the associative superalgebra corresponding to the Lie superalgebra $\mathbf R=\operatorname{Lie}(v_0,v_1)$, where $v_0,v_1$ are defined by the pivot construction referenced in the source. An associative superalgebra $A$ is self-similar if it admits an embedding into a matrix superalgebra tensor $A$, as in the paper. Non-self-similarity conjecture. The associative superalgebra $A$ is not self-similar; likewise, the respective associative superalgebra of the cited example should not be self-similar. The assertions parallel the Lie-superalgebra claim above, and their resolution is left open in the supplied text.