## Ideals in the Goldman Algebra

12 Dec 2017  ·  Nguyen Minh ·

The goal of this work is to study the ideals of the Goldman Lie algebra \$S\$. To do so, we construct an algebra homomorphism from \$S\$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead... The structure \$S\$ can be regarded as either a \$\mathbb{Q}\$-module or a \$\mathbb{Q}\$-module generated by free homotopy classes. For \$\mathbb{Z}\$-module case, we proved that there is an infinite class of ideals of \$S\$ that contain a certain finite set of free homotopy classes. For \$\mathbb{Q}\$-module case, we can classify all the ideals of the new structure and consequently obtain a new class of ideals of the original structure. Finally, we show an interesting infinite chain of ideals that are not those ideals obtained by considering the new structure. read more

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Algebraic Topology Geometric Topology