Classification of subalgebras of the cayley algebra over a finite field

Grishkov A.N.; Giuliani M.D.L.M.; Zavarnitsine A.V.

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Classification of subalgebras of the cayley algebra over a finite field

机译：有限域上的Cayley代数的子代数的分类

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摘要

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F_q, q = p~n. We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

机译：我们对有限域F_q，q = p〜n上的Cayley代数O（q）的所有单位子代数进行分类。我们获得每种类型的子代数的数量，并证明所有同构子代数相对于O（q）的自同构群是共轭的。我们还确定与O（q）的每个子代数相关的Moufang循环的结构。

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《Journal of algebra and its applications》 |2010年第5期|共18页
作者
Grishkov A.N.; Giuliani M.D.L.M.; Zavarnitsine A.V.;
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正文语种 eng
中图分类代数、数论、组合理论;
关键词
automorphism group; Cayley algebra; Moufang loop; subalgebra;

机译：自同构群凯利代数牟芳环次代数;

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专利

1. Classification of subalgebras of the cayley algebra over a finite field [J] . Grishkov A.N., Giuliani M.D.L.M., Zavarnitsine A.V. Journal of algebra and its applications . 2010,第5期

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2. Classification of the maximal subalgebras of exceptional Lie algebras over fields of good characteristic [J] . Alexander Premet, David I. Stewart Journal of the American Mathematical Society . 2019,第4期

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3. Algebraic Cayley graphs over finite fields [J] . M. Lu, D. Wan, L.-P. Wang, Finite fields and their applications . 2014,第jula期

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4. Factorization of polynomials over finite fields and factorization of primes in algebraic number fields [C] . Ming-Deh A. Huang, PMing-Deh A. Huang Annual ACM symposium on Theory of computing;ACM symposium on Theory of computing . 1984

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5. Classification of Five-Dimensional Lie Algebras with One-Dimensional Subalgebras Acting as Subalgebras of the Lorentz Algebra [D] . Rozum, Jordan. 2016

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6. Algebraic complexities and algebraic curves over finite fields [O] . D. V. Chudnovsky, G. V. Chudnovsky 1987

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8. Classification of Graded, Finite-Dimensional Lie Algebras of Vector Fields [R] . Post, G. F. 1993

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Classification of subalgebras of the cayley algebra over a finite field

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