An overview on real division algebras
DOI:
https://doi.org/10.14244/lajm.v2i02.17Palavras-chave:
Real algebras, topological K-theoryResumo
In this paper, we expose initial concepts of real division algebras, providing historical noteson $\R$, $\C$, $\Ham$ and $\Oct$. This is done to emphasize the relevance of topological K-theory
through the Bott-Milnor-Kervaire Theorem, which is at the end. For completeness, we also present
two classical results about the main division algebras.
Referências
Atiyah M. K-theory. Boca Raton: CRC Press; 1967. 240 p.
Baez J C. The Octonions. Bulletin (New Series) of the American Mathematical Society. 2022;39(2): 145-205. DOI: https://doi.org/10.1090/S0273-0979-01-00934-X
Buchmann A. A Brief History of Quaternions and the Theory of Holomorphic Functions of Quaternionic Variables. ArXiv [Internet]. 2011. [cited 2022 Jun 13]; 1111:6088. Available from: https://arxiv.org/abs/1111.6088
Clemente GL. Ordinary and Twisted K-Theory [Thesis (Master’s degree)]. São Carlos: Universidade Federal de São Carlos; 2022 [cited 2022 Jun 10]. 436 p. Available from: https://repositorio.ufscar.br/handle/ufscar/15841
Hatcher A. Vector bundles and K-theory. [book on the internet]. 2017 [cited 2022 Jun 13]. 124 p. Available from: https://pi.math.cornell.edu/~hatcher/VBKT/VB.pdf
Hurwitz A. Über die Composition der quadratischen Formen von beliebig vielen Variabeln, Nachr. Ges. Wiss. Göttingen (1898) pp. 309-316. Available from: https://gdz.sub.uni-goettingen.de/download/pdf/PPN252457811_1898/LOG_0034.pdf
Merino O. A Short History of Complex Numbers. [paper on the internet]. 2006 [cited 2022 Jun 13]. 5 p. Available from: https://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf
Palais R.S. The Classification of Real Division Algebras. American Mathematical Monthly, 1968, 75:366-8. DOI: https://doi.org/10.2307/2313414
Sudbery A. Quaternionic Analysis. Math. Proc. Camb. Phil. Soc. 1979; 85:199-225. DOI: https://doi.org/10.1017/S0305004100055638
Weiss I. The Real Numbers - A Survey of Constructions. ArXiv [Internet]. 2015. [cited 2022 Jun 13]; 1506:03467. Available from: https://arxiv.org/abs/1506.03467,
Zorn M. Theorie der alternativen Ringe, Abh. Math. Sem. Univ. Hamburg 8 (1930), 123-147 p. DOI: https://doi.org/10.1007/BF02940993
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Copyright (c) 2023 Gabriel Longatto Clemente
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.
Os autores podem entrar em acordos contratuais adicionais separados para a distribuição não exclusiva da versão publicada do trabalho da revista (por exemplo, postá-lo em um repositório institucional ou publicá-lo em um livro), com um reconhecimento de sua publicação inicial nesta revista.
