## Dissertations, Master's Theses and Master's Reports

2019

#### Document Type

Open Access Master's Thesis

#### Degree Name

Master of Science in Mathematical Sciences (MS)

Department of Mathematical Sciences

Jie Sun

Melissa Keranen

Fabrizio Zanello

#### Abstract

It was shown by Neher and Sun in [12] that, for perfect Lie superalgebras \$L_i\$, the universal central extension of the direct limit of \$L_i\$ is isomorphic to the direct limit of the universal central extensions of \$L_i\$. In this thesis, we extend the result to Hom-Lie superalgebras, first introduced by Ammar and Makhlouf in [1], and construct the universal central extension of a perfect Hom-Lie superalgebra by defining a \$\uce\$ functor on the category of Hom-Lie superalgebras. In Theorem 4.2.3, we show that if a Hom-Lie superalgebra \$L\$ is perfect, then \$\uce(L)\$ is a universal central extension of \$L\$. In Theorem 4.3.2, we show that the universal central extension of the direct limit of perfect Hom-Lie superalgebras \$L_i\$ is isomorphic to the direct limit of the universal central extensions of \$L_i\$.

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