Some new classes of division algebras and potential applications to spacetime block codingTools Steele, Andrew (2014) Some new classes of division algebras and potential applications to spacetime block coding. PhD thesis, University of Nottingham.
AbstractIn this thesis we study some new classes of nonassociative division algebras. First we introduce a generalisation of both associative cyclic algebras and of Waterhouse's nonassociative quaternions. An important aspect of these algebras is the simplicity of their construction, which is a modification of the classical definition of associative cyclic algebras. By taking the parameter used in the classical definition from a larger field, we lose the property of associativity but gain many new examples of division algebras. This idea is also applied to obtain a generalisation of the first Tits construction.
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