Geodesic
Rational Homogeneous Algebras
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 351-354

Voir la notice de l'article provenant de la source Cambridge University Press

An algebra $A$ is homogeneous if the automorphism group of $A$ acts transitively on the one-dimensional subspaces of $A$ . The existence of homogeneous algebras depends critically on the choice of the scalar field. We examine the case where the scalar field is the rationals. We prove that if $A$ is a rational homogeneous algebra with $\dim\,A\,>\,1$ , then ${{A}^{2}}\,=\,0$ .
DOI : 10.4153/CMB-2011-087-5
Mots-clés : 17D99, 17A36, non-associative algebra, homogeneous, automorphism 
MacDougall, J. A.; Sweet, L. G. Rational Homogeneous Algebras. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 351-354. doi: 10.4153/CMB-2011-087-5
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[1] [1] Djokovič, D. Ž., Real homogeneous algebras. Proc. Amer. Math. Soc. 41(1973), 457–462. Google Scholar

[2] [2] Djokovič, D. Ž. and Sweet, L. G., Infinite homogeneous algebras are anticommutative. Proc. Amer. Math. Soc. 127(1999), no. 11, 3169–3174. Google Scholar | DOI

[3] [3] Djokovič, D. Ž. and Zhao, K., Real homogeneous algebras as truncated division algebras and their automorphism groups. Algebra Colloq. 11(2004), no. 1, 11–20. Google Scholar

[4] [4] Gross, F., Finite automorphic algebras over GF(2) . Proc. Amer. Math. Soc. 31(1972), 10–14. Google Scholar

[5] [5] Ivanov, D. N., Homogeneous algebras over GF(2) . Vestnik Moskov. Univ. Ser. I Mat. Mekh. 1982(1982), 69–72. Google Scholar

[6] [6] Kostrikin, A. I., On homogeneous algebras. Izvestiya Akad. Nauk, SSSR Ser. Mat. 29(1965), 471–484. Google Scholar

[7] [7] Kubota, K. K., Factors of polynomials under composition. J. Number Theory 4(1972), 587–595. Google Scholar | DOI

[8] [8] MacDougall, J. A. and Sweet, L. G., Three dimensional homogeneous algebras. Pacific J. Math. 74(1978), no. 1, 153–162. Google Scholar

[9] [9] Shult, E. E., On the triviality of finite automorphic algebras. Illinois J. Math. 13(1969), 654–659. Google Scholar

[10] [10] Sweet, L. G., On the triviality of homogeneous algebras over an algebraically closed field Proc. Amer. Math. Soc. 48(1975), 321–324. Google Scholar | DOI

[11] [11] Sweet, L. G., On homogeneous algebras. Pacific J.Math 59(1975), no. 2, 385–594. Google Scholar

[12] [12] Sweet, L. G. and MacDougall, J. A., Four-dimensional homogeneous algebras. Pacific J. Math. 129(1987), no. 2, 375–383. Google Scholar

[13] [13] Sweet, L. G. and MacDougall, J. A., A decomposition theorem for homogeneous algebras. J. Austral. Math. Soc. 72(2002), no. 1, 47–56. Google Scholar | DOI

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