| Abstract: | We discuss the question of local finite dimensionality of Jordan supercoalgebras. We establish a connection between Jordan and Lie supercoalgebras which is analogous to the Kantor–Koecher–Tits construction for ordinary Jordan superalgebras. We exhibit an example of a Jordan supercoalgebra which is not locally finite-dimensional. Show that, for a Jordan supercoalgebra (J, ) with a dual algebra J
*, there exists a Lie supercoalgebra (L
c
(J),
L
) whose dual algebra (L
c
(J))* is the Lie KKT-superalgebra for the Jordan superalgebra J
*. It is well known that some Jordan coalgebra J
0 can be constructed from an arbitrary Jordan algebra J. We find necessary and sufficient conditions for the coalgebra (L
c
(J
0),L) to be isomorphic to the coalgebra (Loc(L
in
(J)0),
L
0), where L
in
(J) is the adjoint Lie KKT-algebra for the Jordan algebra J. |
