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arXiv · 1006.4251

The Kantor-Koecher-Tits Construction for Jordan Coalgebras

V. N. Zhelyabin
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Abstract

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

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V. N. Zhelyabin. 2010-06-22. The Kantor-Koecher-Tits Construction for Jordan Coalgebras. https://arxiv.org/abs/1006.4251

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