Dirac cohomology for orthosymplectic superalgebras
by Yupei Zhang
THESIS
2020
Ph.D. Mathematics
vi, 63 pages ; 30 cm
Abstract
In this thesis, we first recall some basic definitions and theorems of Lie algebras
and representations. In particular, we review some background on the irreducible
Harish-Chandra sl(2)-modules and indecomposable sl(2)-modules. Then, we recall
the definitions of Lie superalgebras and the highest weight theory for basic Lie
superalgebras. Especially, we focus on some concrete examples of orthosymplectic
Lie superalgebras. Furthermore, we systematically investigate the Dirac cohomology
for basic Lie superalgebras. At last, we obtain the Dirac cohomology of finite-dimensional
osp(1│2)-modules and the Dirac cohomology of the lowest weight osp(1│2)-modules explicitly.
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