The Kantor-Koecher-Tits Construction for Jordan Coalgebras

Details The Kantor-Koecher-Tits Construction for Jordan Coalgebras The Kantor-Koecher-Tits Construction for Jordan Coalgebras

2010-06-22

arxiv.org/abs/1006.4251v1

Mathematics

Rings and Algebras

Scientific paper

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

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