Inversion of the Covering Map for Indefinite Spin Groups

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Inversion of the Covering Map for Indefinite Spin Groups

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Title: Inversion of the Covering Map for Indefinite Spin Groups
Author(s):
Adjei, Francis
Advisor: Ramakrishna, Viswanath
Date Created: 2017-08
Format: Dissertation
Keywords: Clifford algebras
Group theory
Decomposition (Mathematics)
Abstract: The double covering of Orthogonal groups by the Spin groups is vital for many applications. In this dissertation, we address the important question of inverting the covering map φ_{p,q} : Spin⁺(p,q) → SO⁺(p,q) for (p,q)∈ (2,1),(2,2),(3,1),(3,2),(3,3) in the indefinite case. We also develop explicit formulae for the forward map φ_{p,q} : Spin⁺(p,q) → SO⁺(p,q) for (p,q)∈ (1,2),(1,3),(2,3). We do not work with the even subalgebra of Cl(p,q) and thus our formulae are quite explicit. Our method relies significantly on standard Givens and hyperbolic Givens.
Degree Name: PHD
Degree Level: Doctoral
Persistent Link: http://hdl.handle.net/10735.1/5472
Type : text
Degree Program: Mathematics

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