FROBENIUS AND HURWITZ THEOREMS ABOUT REAL DIVISION ALGEBRAS

Authors

DOI:

https://doi.org/10.47820/recima21.v4i7.3594

Keywords:

the algebras of the complexes C, of the quaternions

Abstract

This work aims to present a proximity between the algebras of the complexes C, of the quaternions H, of the octonions O with the algebra of reals R. To do so, we will describe tools for the demonstrations of the theorems of Frobenius and Hurwitz, where the first one says that the algebras R,  C e H are the only divisions algebras over the reals where multiplications is associative (such as algebras are called
associative) and the second states that algebras R,  C,  H and O are the only ones division algebras
with identity element in which it is possible to define a norm compatible with the multiplication.

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Author Biographies

  • Lia Nojosa Sena
    Master in Mathematics from the Federal University of Ceará.
  • Rubens Cainan Saboia Monteiro
    Master in Mathematics from the Federal University of Ceará.
  • Maria Madalena de Queiroz Alves

    Graduada no bacharelado em ciência da computação no Instituto Federal de Educação, Ciência e Tecnologia do Ceará, campus Tianguá.

References

EBBINGHAUS, H.-D.; HERMES, H.; HIRZEBRUCH, F.; KOECHER, M.; MAINZER, K.; NEUKIRCH, J.; PRESTEL, A.; REMMERT, R. Graduate Texts in Mathematics, Readings in Mathematics: Numbers. New York: Springer, 1991.

FELZENSZWALB, B. Álgebra de dimensão finitas. Rio de Janeiro: IMPA, 1979.

KANTOR, I. L; SOLODOVNIKOV, A. S. Hypercomplex Numbers: An elementary introduction to Algebras. New York, 1989.

Published

26/07/2023

How to Cite

FROBENIUS AND HURWITZ THEOREMS ABOUT REAL DIVISION ALGEBRAS . (2023). RECIMA21 - Revista Científica Multidisciplinar - ISSN 2675-6218, 4(7), e473594. https://doi.org/10.47820/recima21.v4i7.3594