A construction for coisotropic subalgebras of Lie bialgebras

TL;DR

This paper introduces an explicit method for constructing coisotropic subalgebras within Lie bialgebras, providing concrete examples for classical complex simple Lie algebras, advancing understanding of their substructure.

Contribution

It presents a new explicit construction procedure for coisotropic subalgebras in Lie bialgebras, with detailed examples for classical complex simple Lie algebras.

Findings

Explicit construction method for coisotropic subalgebras

Families of examples for classical complex simple Lie algebras

Enhanced understanding of Lie bialgebra substructures

Abstract

Given a Lie bialgebra (g,g*), we present an explicit procedure to construct coisotropic subalgebras, i.e. Lie subalgebras of g whose annihilator is a Lie subalgebra of g*. We write down families of examples for the case that g is a classical complex simple Lie algebra.