Abstract
Nonassociative quaternion algebras were first discovered over the real numbers independently by Dickson and Albert and provided some of the first examples of nonassociative division algebras. They were later classified completely by Waterhouse.
Cyclic algebras can be seen as a natural generalisation of the classical quaternion algebras. With this in mind we generalise nonassociative quaternion algebras and introduce nonassociative cyclic algebras. These provide new examples of nonassociative central division algebras with Nucleus a separable field extension of degree n.
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I would like to thank Susanne Pumplün for suggesting this topic to me and for her many helpful comments throughout.
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Steele, A. Nonassociative cyclic algebras. Isr. J. Math. 200, 361–387 (2014). https://doi.org/10.1007/s11856-014-0021-7
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DOI: https://doi.org/10.1007/s11856-014-0021-7