Results 31 to 40 of about 1,018 (285)
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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Levels and sublevels of composition algebras
, 2007 Lewis' and Leep's bounds on the level and sublevel of quaternion algebras are extended to the class of composition algebras. Some simple constructions of composition algebras of known level values are given.
O'Shea, James
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Free integro-differential algebras and Groebner-Shirshov bases [PDF]
, 2014 The notion of commutative integro-differential algebra was introduced for the algebraic study of boundary problems for linear ordinary differential equations. Its noncommutative analog achieves a similar purpose for linear systems of such equations.
Guo, Li +5 more
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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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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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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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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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Advanced Engineering Materials, EarlyView.A numerical model resulting from irreversible thermodynamics for describing transport processes is introduced, focusing on thermodynamic activity gradients as the actual driving force for diffusion. Implemented in CUDA C++ and using CalPhaD methods for determining the necessary activity data, the model accurately simulates interdiffusion in aluminum ...
Ulrich Holländer +3 more
wiley +1 more source
, 2021 The aim of this work is to study the Hamiltonian quaternions H and quaternion alge- bras. The first two chapters are based on the article Quaternion algebras by K. Conrad and the rest on the book Quaternion algebras by J. Voight.
Mišlanová, Kristína
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