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New central elements in free alternative algebras. / Shestakov, Ivan; Sverchkov, Sergei.

в: Israel Journal of Mathematics, 21.08.2024, стр. 1-26.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

Harvard

Shestakov, I & Sverchkov, S 2024, 'New central elements in free alternative algebras', Israel Journal of Mathematics, стр. 1-26. https://doi.org/10.1007/s11856-024-2650-9

APA

Shestakov, I., & Sverchkov, S. (2024). New central elements in free alternative algebras. Israel Journal of Mathematics, 1-26. https://doi.org/10.1007/s11856-024-2650-9

Vancouver

Shestakov I, Sverchkov S. New central elements in free alternative algebras. Israel Journal of Mathematics. 2024 авг. 21;1-26. doi: 10.1007/s11856-024-2650-9

Author

Shestakov, Ivan ; Sverchkov, Sergei. / New central elements in free alternative algebras. в: Israel Journal of Mathematics. 2024 ; стр. 1-26.

BibTeX

@article{41441f9f9a8f4f659bda9899c8b64bb6,
title = "New central elements in free alternative algebras",
abstract = "A new series of central elements is found in the free alternative algebra. More exactly, let Alt[X] and SMalc[X] ⊂ Alt[X] be the free alternative algebra and the free special Malcev algebra over a field of characteristic 0 on a set of free generators X, and let f (x, y, x1,…, xn) ∈ SMalc[X] be a multilinear element which is trivial in the free associative algebra. Then the element un = un (x, x1,…,xn) = f (x2, x, x1,…,xn) − f (x, x2,x1,…,xn) lies in the center of the algebra Alt[X]. The elements un(x, x1,…, xn) are uniquely defined up to a scalar for a given n (that is, they do not depend on f but only on deg f), and they are skew-symmetric on the variables x1,…,xn. Moreover, un = 0 for n = 4m + 2, 4m + 3 and un ≠ 0 for n = 4m, 4m + 1. The ideals generated by the elements u4m, u4m+1 lie in the associative center of the algebra Alt[X] and have trivial multiplication.",
author = "Ivan Shestakov and Sergei Sverchkov",
note = "The first author was supported by the Mathematical Center in Akademgorodok, agreement with the Ministry of Science and Higher Education of the Russian Federation No. 075-15-2022-281. He was also partially supported by FAPESP, Proc. 2018/23690-6 and CNPq, Proc. 304313/2019-0 of Brazil. The second author was partially supported by FAPESP, Proc. 2018/03717-7 of Brazil.",
year = "2024",
month = aug,
day = "21",
doi = "10.1007/s11856-024-2650-9",
language = "English",
pages = "1--26",
journal = "Israel Journal of Mathematics",
issn = "0021-2172",
publisher = "Springer New York",

}

RIS

TY - JOUR

T1 - New central elements in free alternative algebras

AU - Shestakov, Ivan

AU - Sverchkov, Sergei

N1 - The first author was supported by the Mathematical Center in Akademgorodok, agreement with the Ministry of Science and Higher Education of the Russian Federation No. 075-15-2022-281. He was also partially supported by FAPESP, Proc. 2018/23690-6 and CNPq, Proc. 304313/2019-0 of Brazil. The second author was partially supported by FAPESP, Proc. 2018/03717-7 of Brazil.

PY - 2024/8/21

Y1 - 2024/8/21

N2 - A new series of central elements is found in the free alternative algebra. More exactly, let Alt[X] and SMalc[X] ⊂ Alt[X] be the free alternative algebra and the free special Malcev algebra over a field of characteristic 0 on a set of free generators X, and let f (x, y, x1,…, xn) ∈ SMalc[X] be a multilinear element which is trivial in the free associative algebra. Then the element un = un (x, x1,…,xn) = f (x2, x, x1,…,xn) − f (x, x2,x1,…,xn) lies in the center of the algebra Alt[X]. The elements un(x, x1,…, xn) are uniquely defined up to a scalar for a given n (that is, they do not depend on f but only on deg f), and they are skew-symmetric on the variables x1,…,xn. Moreover, un = 0 for n = 4m + 2, 4m + 3 and un ≠ 0 for n = 4m, 4m + 1. The ideals generated by the elements u4m, u4m+1 lie in the associative center of the algebra Alt[X] and have trivial multiplication.

AB - A new series of central elements is found in the free alternative algebra. More exactly, let Alt[X] and SMalc[X] ⊂ Alt[X] be the free alternative algebra and the free special Malcev algebra over a field of characteristic 0 on a set of free generators X, and let f (x, y, x1,…, xn) ∈ SMalc[X] be a multilinear element which is trivial in the free associative algebra. Then the element un = un (x, x1,…,xn) = f (x2, x, x1,…,xn) − f (x, x2,x1,…,xn) lies in the center of the algebra Alt[X]. The elements un(x, x1,…, xn) are uniquely defined up to a scalar for a given n (that is, they do not depend on f but only on deg f), and they are skew-symmetric on the variables x1,…,xn. Moreover, un = 0 for n = 4m + 2, 4m + 3 and un ≠ 0 for n = 4m, 4m + 1. The ideals generated by the elements u4m, u4m+1 lie in the associative center of the algebra Alt[X] and have trivial multiplication.

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U2 - 10.1007/s11856-024-2650-9

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M3 - Article

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JO - Israel Journal of Mathematics

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