  The paper concerns extra special associative algebras, an analogue of the
Heisenberg Lie algebra. In particular, we say that an associative algebra is
extra special if its center is equal to its derived ideal and the center is
1-dimensional. In this paper, we classify extra special associative algebras by
proving that their structure is equivalent to that of extra special Leibniz
algebras. We then characterize their (Schur) multipliers via dimension and
completely determine their capability. We connect this with the related notion
of unicentral algebras and discuss the problem of classifying extra special
diassociative algebras.
