Titlebook: Quaternion Algebras; John Voight Textbook‘‘‘‘‘‘‘‘ 2021 The Editor(s) (if applicable) and The Author(s) 2021 Open Access.Quaternions.Quater

肿块

BeginningsIn this chapter, we define quaternion algebras over fields by giving a multiplication table, following Hamilton; we then consider the classical application of understanding rotations in ..

Sad570

InvolutionsIn this chapter, we define the standard involution on a quaternion algebra. In this way, we characterize division quaternion algebras as noncommutative division rings equipped with a standard involution.

保全

山羊

Ternary quadratic forms and quaternion algebrasContinuing our treatment of quadratic forms, in this chapter we connect quaternion algebras to ternary quadratic forms.

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腐烂

Ternary quadratic forms over local fieldsIn this chapter, we classify quaternion algebras over local fields using quadratic forms; this generalizes the classification of quaternion algebras over ..

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谁在削木头

Quaternion algebras over global fieldsTo motivate the classification of quaternion algebras over ., we consider by analogy a classification of quadratic fields. We restrict to the following class of quadratic fields for the best analogy.