I biquaternioni di Hamilton e di Clifford e i bicomplessi di Segre: origini, confronti e applicazioni

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Abstract

[automatically translated] RW Hamilton, already in 1850, had developed an extension of the quaternions, defining the algebra of biquaternioni. In that year, he made the subject of a communication to the meeting of the British Association for the Advancement of Science in Edinburgh, of which there remain only the Report. Subsequently, in 1853 in "Lectures on quaternions" re-introduced the biquaternioni as imaginary solutions of quadratic equations with coefficients in quaternions. In 1866, in the Elements of quaternions, work published posthumously, Hamilton returned to the subject and introduced the "biquaternioni coplanar" as solutions of equations with coefficients in "quaternions coplanar" that is, under the form of algebra "bicomplessi" as C. Segre defined in 1891 in the context of the study of algebra and geometry on complex: "The introduction of imaginari points in geometry corresponds to the introduction of imaginari numbers (coordinates) in the analysis. Before Segre, in 1873 W. Clifford, he introduced two other "biquaternioni". and later in 1878 it will define the ones we know as "Clifford Algebras", which generalize the quaternions and have applications in physics.
Original languageItalian
Number of pages1
Publication statusPublished - 2015

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