Date of Award
2019
Document Type
Open Access Master's Thesis
Degree Name
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Jie Sun
Committee Member 1
Melissa Keranen
Committee Member 2
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 $L_i$.
Recommended Citation
Bigler, Dale, "Universal Central Extensions of Direct Limits of Hom-Lie Superalgebras", Open Access Master's Thesis, Michigan Technological University, 2019.
