Coisotropic subalgebras of complex semisimple Lie bialgebras

Kroeger, Nicole

doi:10.1090/proc12710

Coisotropic subalgebras of complex semisimple Lie bialgebras
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Proc. Amer. Math. Soc. 144 (2016), 473-486 Request permission

Abstract:

In his paper “A Construction for Coisotropic Subalgebras of Lie Bialgebras”, Marco Zambon gave a way to use a long root of a complex semisimple Lie bialgebra $\mathfrak {g}$ to construct a coisotropic subalgebra of $\mathfrak {g}$. In this paper, we generalize Zambon’s construction. Our construction is based on the theory of Lagrangian subalgebras of the double $\mathfrak {g}\oplus \mathfrak {g}$ of $\mathfrak {g}$, and our coisotropic subalgebras correspond to torus fixed points in the variety $\mathcal {L}(\mathfrak {g}\oplus \mathfrak {g})$ of Lagrangian subalgebras of $\mathfrak {g}\oplus \mathfrak {g}$.

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