Results 1 to 10 of about 542 (165)
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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Wiener Algebra for the Quaternions [PDF]
Mediterranean Journal of Mathematics, 2015 We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener-Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener-Hopf operators.
Alpay, Daniel +3 more
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Quaternion Algebras and Generalized Fibonacci–Lucas Quaternions [PDF]
Advances in Applied Clifford Algebras, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flaut, Cristina, Savin, Diana
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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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, 2021 This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature.
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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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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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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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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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