  We compare a number of different definitions of structure algebras and TKK
constructions for Jordan (super)algebras appearing in the literature. We
demonstrate that, for unital superalgebras, all the definitions of the
structure algebra and the TKK constructions fall apart into two cases.
Moreover, one can be obtained as the Lie superalgebra of superderivations of
the other. We also show that, for non-unital superalgebras, more definitions
become non-equivalent. As an application, we obtain the corresponding Lie
superalgebras for all simple finite dimensional Jordan superalgebras over an
algebraically closed field of characteristic zero.
