Low-Dimensional Quaternionic Matrix Groups
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Authors
Machen, Casey J.
Issue Date
2011
Type
Thesis
Language
en_US
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Abstract
We focus on several properties of the Lie groups Sp(n) and SLn(H). We discuss their
Lie algebras, the exponential map from the Lie algebras to the groups, as well as
when this map is surjective. Since quaternionic multiplication is not commutative,
the process of calculating the exponential of a matrix in Sp(n) or SLn(H) is more
involved than the process of calculating the exponential of a matrix over the real or
complex numbers. We develop processes by which this calculation may be reduced to
a simpler problem, and provide an example to illustrate this. Additionally, we discuss
properties of these groups such as centers, maximal tori, normalizers of the maximal
tori, Weyl groups, and Clifford Algebras.
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In Copyright(All Rights Reserved)