Coisotropic Subalgebras of Complex Semisimple Lie Bialgebras

2014/09/03 by Kroeger, Nicole
#17B62 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1409.1183

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 biaglebra \mathfrakg to construct a coisotropic subalgebra of \mathfrakg. In this paper, we generalize Zambon's construction. Our construction is based on the theory of Lagrangian subalgebras of the double \mathfrakg⊕\mathfrakg of \mathfrakg, and our coisotropic subalgebras correspond to torus fixed points in the variety L(\mathfrakg⊕\mathfrakg) of Lagrangian subalgebras of \mathfrakg⊕\mathfrakg.

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