Results 141 to 150 of about 122,808 (179)
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On the quaternionic Weyl algebra
Advances in Applied Clifford Algebras, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
SABADINI, IRENE MARIA, D. Struppa
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Quaternion Group Algebra and Representations of the Quaternions [PDF]
Communications in Algebra, 2019 AbstractIn this paper, we provide a concrete and explicit decomposition of the quaternion group algebra through a suitable basis of the algebra.
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2003
One of the main aims of this chapter is to complete the classification theorem for quaternion algebras over a number field by establishing the existence part of that theorem. This theorem, together with other results in this chapter, make use of the rings of adeles and groups of ideles associated to number fields and quaternion algebras.
Colin Maclachlan, Alan W. Reid
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One of the main aims of this chapter is to complete the classification theorem for quaternion algebras over a number field by establishing the existence part of that theorem. This theorem, together with other results in this chapter, make use of the rings of adeles and groups of ideles associated to number fields and quaternion algebras.
Colin Maclachlan, Alan W. Reid
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Journal of Mathematical Sciences, 1995
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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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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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An Embedding Theorem for Quaternion Algebras
Journal of the London Mathematical Society, 1999We 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 Algebraic Riccati Equation for Quaternions
Advances in Applied Clifford Algebras, 2013The 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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The Lengths of the Quaternion and Octonion Algebras
Journal of Mathematical Sciences, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guterman, Alexander E. +1 more
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On Zeta Functions of Quaternion Algebras
The Annals of Mathematics, 1965The 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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