The Kantor-Koecher-Tits construction for Jordan coalgebras
The relationship between Jordan and Lie coalgebras
is established. We prove that from any Jordan coalgebra J
it is possible to construct a Lie coalgebra
L(J). Moreover, any dual algebra of the
coalgebra L(J) corresponds to a Lie
algebra that can be determined from the dual algebra for J,
following the Kantor-Koecher-Tits process. The
structure of subcoalgebras and coideals of the coalgebra
L(J) is characterized.
V. N. Zhelyabin <vivnic@math.nsc.ru>