Results 211 to 220 of about 271 (247)

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
exaly  

Jordan constants of quaternion algebras over number fields and simple abelian surfaces over fields of positive characteristic

Mathematische Nachrichten, 2022
Wontae Hwang
exaly  

Rank one sheaves over quaternion algebras on Enriques surfaces

Advances in Geometry, 2022
Fabian Reede
exaly  

Submodules of Quaternion Algebras

Proceedings of the London Mathematical Society, 1969
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