Geodesic
On Mizuhara's construction for endomorphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 41-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider Mizuhara's construction for the endomorphs. It is shown that this construction gives almost simple algebras, which are used to construct new examples of simple right-symmetric algebras. To investigate the Mizuhara extensions we give a description of the derivations of the endomorphs constructed on nonunital algebras, which generalizes a result obtained earlier in the unital case.
Keywords: right-symmetric algebra, simple algebra, pre-Lie algebra, endomorph, derivation.
Mots-clés : Mizuhara's construction 
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A. P. Pozhidaev. On Mizuhara's construction for endomorphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 41-54. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a0/

[1] A. Mizuhara, “On simple left symmetric algebras over a solvable Lie algebra”, Sci. Math. Jpn., 57:2 (2003), 325–337 | MR | Zbl

[2] A.P. Pozhidaev, “On generalized Mizuhara's construction”, Sib. Math. J., 2023 | MR

[3] H. Shima, “Homogenous Hessian manifold”, Ann. Inst. Fourier, 30 (1980), 91–128 | DOI | MR | Zbl

[4] A.P. Pozhidaev, “On endomorphs of right-symmetric algebras”, Sib. Math. J., 61:5 (2020), 859–866 | DOI | MR | Zbl

[5] R. Słowik, “Derivations of rings of infinite matrices”, Commun. Algebra, 43:8 (2015), 3433–3441 | DOI | MR | Zbl