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Orders of quaternion algebras with involution

Journal of Number Theory, 2018
We introduce the notion of maximal orders over quaternion algebras with orthogonal involution and give a classification over local fields, and a partial classification over algebraic number fields.
Arseniy Sheydvasser
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On quaternion algebras

Journal of Mathematical Sciences, 1995
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Algebraic Riccati Equation for Quaternions

Advances in Applied Clifford Algebras, 2013
The paper studies a Riccati equation \[ p(x):=a+bx+xc+xdx=0,\qquad a,b,c,d,x \in \mathbb{H}, \] where \(p\) is a quaternionic polynomial, which is shown to be reducible to a one-sided type. The set of quaternions \( \mathbb{H}\) can be seen as the four-dimensional vector space \( \mathbb{R}^4\) equipped with a special multiplication rule.
Janovská, Drahoslava, Opfer, Gerhard
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An Embedding Theorem for Quaternion Algebras

Journal of the London Mathematical Society, 1999
We prove an integral version of a classical embedding theorem concerning quaternion algebras \(B\) over a number field \(k\). Assume \(B\) satisfies the Eichler condition, i.e. that some infinite place of \(k\) is not ramified in \(B\), and let \(\Omega\) be an order in a quadratic extension of \(k\). We determine which maximal orders of \(B\) admit an
Chinburg, Ted, Friedman, Eduardo
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The algebra of quaternions

2014
This chapter concerns (scalar) quaternions and the basic properties of quaternion algebra, with emphasis on solution of equations such as axb = c and ax − xb =
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The Lengths of the Quaternion and Octonion Algebras

Journal of Mathematical Sciences, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guterman, Alexander E., Kudryavtsev, D. K.   +1 more
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Algebras, Quaternions and Quaternionic Symplectic Groups

2002
In this chapter we begin by studying algebras over a field, with their groups of units providing many interesting groups. In particular, we study division algebras and their linear algebra. Then we introduce the quaternions which form the only non-commutative example of a real division algebra.
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On Zeta Functions of Quaternion Algebras

The Annals of Mathematics, 1965
The present paper is concerned with some equalities between zeta functions of quaternion algebras introduced in Godement [6], Shimura [11], Tamagawa [13]. Let A be a quaternion algebra over a totally real algebraic number field 1? of degree m, and let D be an order in A; let S be the idele group of A, and U the group of units in S with respect to D ...
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Linkage of sets of quaternion algebras in characteristic 2

Communications in Algebra, 2021
Adam Chapman
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Jordan constants of quaternion algebras over number fields and simple abelian surfaces over fields of positive characteristic

Mathematische Nachrichten, 2022
Wontae Hwang
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