A note on simple, 4-dimensional, ternary Filippov algebras
DOI:
https://doi.org/10.5269/bspm.75376Resumen
Properties of simple, 4-dimensional, ternary Filippov algebras are presented. More concretely, 1-identities and 2-identities, conservativeness and some equations are studied.
Referencias
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2. Bai, R.-P., Wu, Y., Constructions of 3-Lie algebras, Linear Multilinear Algebra 63, 2171-2186, (2015).
3. Beites, P. D., Nicolas, A. P., An associative triple system of the second kind, Comm. Algebra 44, 5027-5043, (2016).
4. Beites, P. D., Nicolas, A. P., Pozhidaev, A. P., Saraiva, P., On identities of a ternary quaternion algebra, Comm. Algebra 39, 830-842, (2011).
5. Bremner, M. R., Hentzel, I., Invariant nonassociative algebra structures on irreducible representations of simple Lie algebras, Exp. Math. 13, 231-256, (2003).
6. Filippov, V. T., n-Lie algebras, Sib. Math. J. 26, 879-891, (1985).
7. Kantor, I. L., Terminal trilinear operations, Algebra Logic 28, 25-40, (1989).
8. Kasymov, S. M., Theory of n-Lie algebras, Algebra Logic 26, 155-166, (1987).
9. Kaygorodov, I., (n + 1)-Ary derivations of semisimple Filippov algebras, Math. Notes 96, 208-216, (2014).
10. Kaygorodov, I., Lopatin, A., Popov, Y., Conservative algebras of 2-dimensional algebras, Linear Algebra Appl. 486, 255-274, (2015).
11. Ling, W., On the structure of n-Lie algebras, PhD Thesis, (1993).
12. Nambu, Y., Generalized Hamiltonian dynamics, Phys. Rev. D 7, 2405-2412, (1973).
13. Saraiva, P., Reduced n-Lie algebras, Comm. Algebra 30, 2057-2074, (2002).
14. Saraiva, P., On some generalizations of Malcev algebras, Int. J. Math. Game Theory Algebra 13, 89-108, (2002).
15. Takhtajan, L., On foundation of the generalized Nambu mechanics, Comm. Math. Phys. 160, 295-315, (1994).
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Publicado
2025-04-30
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Research Articles
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When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Cómo citar
Beites, P., & Nicolás, A. (2025). A note on simple, 4-dimensional, ternary Filippov algebras. Boletim Da Sociedade Paranaense De Matemática, 43, 1-6. https://doi.org/10.5269/bspm.75376
