The Kantor-Koecher-Tits Construction for Jordan Coalgebras

Abstract

The relationship between Jordan and Lie coalgebras is established. We prove that from any Jordan coalgebra $⟨A,\Delta ⟩$, it is possible to construct a Lie coalgebra $⟨L(A),{\Delta }_L⟩$. Moreover, any dual algebra of the coalgebra $⟨L(A),{\Delta }_L⟩$ corresponds to a Lie algebra that can be determined from the dual algebra for $⟨A,\Delta ⟩$, following the Kantor--Koecher--Tits process. The structure of subcoalgebras and coideals of the coalgebra $⟨L(A),{\Delta }_L⟩$ is characterized.