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On automorphisms of quaternion orders. (English) Zbl 0678.16003

The paper contains a description of automorphism groups of quaternion Bass orders over complete discrete valuation rings of characteristic \(\neq 2\). Using this description, the numbers of optimal embeddings of quadratic orders over local rings into quaternion Bass orders over such rings modulo the action of the unit groups are computed. As an application, a formula for class numbers of arbitrary quaternion orders in definite quaternion algebras over the rational numbers is proved.
Reviewer: J.Brzezinski

MSC:

16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
16W20 Automorphisms and endomorphisms
16Kxx Division rings and semisimple Artin rings
11R52 Quaternion and other division algebras: arithmetic, zeta functions
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