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Structure fractals and para-quaternionic geometry

Julian ŁawrynowiczMassimo Vaccaro — 2011

Annales UMCS, Mathematica

It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2, 4 and 8, respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 27. Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of...

Structure fractals and para-quaternionic geometry

Julian ŁawrynowiczMassimo Vaccaro — 2011

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

It is well known that starting with real structure, the Cayley-Dickson process gives complex, quaternionic, and octonionic (Cayley) structures related to the Adolf Hurwitz composition formula for dimensions p = 2 , 4 and 8 , respectively, but the procedure fails for p = 16 in the sense that the composition formula involves no more a triple of quadratic forms of the same dimension; the other two dimensions are n = 2 7 . Instead, Ławrynowicz and Suzuki (2001) have considered graded fractal bundles of the flower type related...

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