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
Terms of Use: Copyright ©2017 is held by the author. Digital access to this material is made possible by the Eugene McDermott Library. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Type : text
Degree Program: Mathematics

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