On the semi-infinite cohomology and categorification of the Boson-Fermion correspondence
by Choy Ka Hei
THESIS
2023
M.Phil. Mathematics
1 online resource (vii, 80 pages) : illustrations
Abstract
In this thesis, we first examine the algebraic setting for the semi-infinite cohomology
of a Lie algebra and then discuss the realization of semi-infinite cohomology
by means of quantum groups. Next, we introduce the original bosonfermion
correspondence and its categorification introduced by Frenkel, Penkov
and Serganova. We then use the construction to categorify the Weyl algebra and
Clifford algebra and their corresponding identities. Finally, we suggest possible
future directions for these two topics.
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