Results 31 to 40 of about 122,808 (179)
On quaternion applications in obtaining surfaces
4 open, 2019 In this paper, we survey the historical development of quaternions and give some recently studies and applications of quaternions of obtaining surfaces.
Keskin Özgür, Yaylı Yusuf
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Quaternion Algebras and the Algebraic Legacy of Hamilton's Quaternions
Irish Mathematical Society Bulletin, 2006 We describe the basic definitions and fundamen- tal properties of quaternion algebras over fields and proceed to give an account of how Hamilton's 1843 discovery of the quaternions was a major turning point in the subject of al- gebra. Noncommutative algebra started here! We will em- phasize especially the theory of division algebras and other kinds of
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On separable extensions of group rings and quaternion rings
International Journal of Mathematics and Mathematical Sciences, 1978 The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG(R may be a non-commutative ring), and (2) to give a full description of the set ...
George Szeto
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Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry
Physics Letters B, 2017 We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four “magical” Jordan algebras of 3×3 ...
J. Ambjørn, Y. Watabiki
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Computing square roots in quaternion algebras [PDF]
, 2023 We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.Comment: Final version of the paper formatted by the editorial board to appear in Fundamenta ...
Koprowski, Przemysław
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Linear Algebra and its Applications, 1984 Let k be a field of characteristic not equal to 2, and let L be a finite field extension of k. Then a Lie algebra G is quaternionic if there is a quaternion division algebra Q over L such that G is isomorphic to the k- Lie-algebra \(Q^-/L1\). The main theorem of the paper gives equivalent conditions for a finite-dimensional Lie algebra over a perfect ...
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On the linkage of quaternion algebras
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2002 Let \(B\) and \(C\) be quaternion algebras over a field \(F\). A well known theorem [\textit{A. A. Albert}, Proc. Am. Math. Soc. 35, 65-66 (1972; Zbl 0263.16012), \textit{C.-H. Sah}, J. Algebra 20, 144-160 (1972; Zbl 0226.15010)] states that \(B\otimes_FC\) is a division algebra if and only if \(B\) and \(C\) have no common quadratic splitting field ...
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The “fundamental theorem of algebra” for quaternions [PDF]
Bulletin of the American Mathematical Society, 1944 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eilenberg, Samuel, Niven, Ivan
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Generalized Quaternions and Matrix Algebra
Afyon Kocatepe University Journal of Sciences and Engineering, 2023 In this paper, we established the connection between generalized quaternion algebra and real (complex) matrix algebras by using Hamilton operators. We obtained real and complex matrices corresponding to the real and complex basis of the generalized quaternions. Also, we investigated the basis features of real and complex matrices. We get Pauli matrices
Erhan ATA, Ümit Ziya SAVCI
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Selectivity in quaternion algebras
Journal of Number Theory, 2012 We prove an integral version of the classical Albert-Brauer-Hasse-Noether theorem regarding quaternion algebras over number fields. Let $\mathfrak A$ be a quaternion algebra over a number field $K$ and assume that $\mathfrak A$ satisfies the Eichler condition; that is, there exists an archimedean prime of $K$ which does not ramify in $\mathfrak A$. Let
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