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Generalized quaternion algebras
Rendiconti del Circolo Matematico di Palermo Series 2, 2023This paper is part of a small but growing circle of papers (including [\textit{E. Kizil} and \textit{Y. Alagöz}, Turk. J. Math. 43, No. 5, 2649--2657 (2019; Zbl 1431.16047)]) that study something they call ``generalized quaternion algebras'', which originate in [\textit{A. Mamagani} and \textit{M.
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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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Journal of Mathematical Sciences, 1995
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Generalized quaternion algebras
Mathematical Notes, 1993Es sei \(A\) ein kommutativer Ring, in dem 2 invertierbar ist. Zu invertierbaren Elementen \(a,b\in A\) sei \(Q=(a,b/A)\) die verallgemeinerte Quaternionenalgebra. Der Verf. zeigt, daß \(Q\) genau dann rechtsdistributiv ist, wenn \(A\) distributiv und die quadratische Form \(x^2-ay^2-bz^2\) nullteilig modulo jedem maximalen Ideal \(M\) von \(A\) ist ...
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Algebras, Quaternions and Quaternionic Symplectic Groups
2002In 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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2003
The basic algebraic theory of quaternion algebras was given in Chapter 2. That sufficed for the results obtained so far on deducing information on a Kleinian group Γ from its invariant trace field kΓ and invariant quaternion algebra AΓ. We have yet to expound on the arithmetic theory of quaternion algebras over number fields.
Colin Maclachlan, Alan W. Reid
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The basic algebraic theory of quaternion algebras was given in Chapter 2. That sufficed for the results obtained so far on deducing information on a Kleinian group Γ from its invariant trace field kΓ and invariant quaternion algebra AΓ. We have yet to expound on the arithmetic theory of quaternion algebras over number fields.
Colin Maclachlan, Alan W. Reid
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Archiv der Mathematik, 2008
The level of a ring R with 1 ≠ 0 is the smallest positive integer s such that −1 can be written as a sum of s squares in R, provided −1 is a sum of squares at all. D. W. Lewis showed that any value of type 2n or 2n + 1 can be realized as level of a quaternion algebra, and he asked whether there exist quaternion algebras whose levels are not of that ...
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The level of a ring R with 1 ≠ 0 is the smallest positive integer s such that −1 can be written as a sum of s squares in R, provided −1 is a sum of squares at all. D. W. Lewis showed that any value of type 2n or 2n + 1 can be realized as level of a quaternion algebra, and he asked whether there exist quaternion algebras whose levels are not of that ...
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Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization
Chemical Reviews, 2022Christos Xiouras +2 more
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