La strana storia degli ottonioni: dalla Teoria delle Algebre alle applicazioni in Fisica

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Abstract

[automatically translated] "The history of mathematics has shown repeatedly that discard a beautiful and profound theory only because it does not seem to have immediate applications is a bad move" [I. Stewart] The work presented here concerns a particular algebraic structure and 'the perfect illustration of the meaning of the sentence quoted. The octonions, born in a pure mathematical research context on hypercomplex number systems, paved the way for the emergence of the general concept of "algebraic structure". Therefore, it seemed that their role was simply to be an example of non-associative structure within Modern Algebra and even the same Cayley after they introduced "you forget '' them for about 30 years. Contrary to Quaternions, born in the same context and almost simultaneously, octonions seemed that they had no immediate geometric interpretation or other sciences applications. You have to get that from the first half of the twentieth century to find the first mission critical applications to projective geometry to the theory of Lie algebras. Surprisingly, in the eighties he saw one of their connection with the theory of strings, which has brought again at the center of scientific research and made them them today protagonists of many books both popular and technical as "The elegance of the truth. History of Symmetry "by I. Stewart and" On quaternions and octonions "JH Conway and DA Smith. You have to get that from the first half of the twentieth century to find the first mission critical applications to projective geometry to the theory of Lie algebras. Surprisingly, in the eighties he saw one of their connection with the theory of strings, which has brought again at the center of scientific research and made them them today protagonists of many books both popular and technical as "The elegance of the truth. History of Symmetry "by I. Stewart and" On quaternions and octonions "JH Conway and DA Smith. You have to get that from the first half of the twentieth century to find the first mission critical applications to projective geometry to the theory of Lie algebras. Surprisingly, in the eighties he saw one of their connection with the theory of strings, which has brought again at the center of scientific research and made them them today protagonists of many books both popular and technical as "The elegance of the truth. History of Symmetry "by I. Stewart and" On quaternions and octonions "JH Conway and DA Smith. who brought again at the center of scientific research and made them them today protagonists of many books both popular and technical as "The elegance of the truth. History of Symmetry "by I. Stewart and" On quaternions and octonions "JH Conway and DA Smith. who brought again at the center of scientific research and made them them today protagonists of many books both popular and technical as "The elegance of the truth. History of Symmetry "by I. Stewart and" On quaternions and octonions "JH Conway and DA Smith.
Original languageItalian
Pages (from-to)21-27
Number of pages6
JournalLETTERA MATEMATICA PRISTEM
Volume76
Publication statusPublished - 2010

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